The golfing world accepted the 1899 R&A rules code, including the recently-formed USGA who followed the R&A code, adjusted and clarified with its own decisions and remarks.

The increased popularity of the game gave rise to many disputes and queries over the rules, leading to the R&A issuing the first Decisions book in 1908, and in the 1920s, the USGA did the same.

The first difference of opinion was not long in coming: the centre-shafted putter. More on that, and on the differences in the size and weight of the ball in Clubs and Balls.

In addition to the differences over equipment, some other differences between the R&A and USGA came over the years, fortunately nearly all minor ones.

One thorny issue, though, was the stymie. The USGA in 1920-1 tried allowing a player to concede an opponent's putt when stymied.
In 1938-39 they trialled a modification to the stymie rule by allowing a player to have an opponent's ball, within six inches of the hole, lifted. This was made permanent in 1941.
In 1950 the USGA abolished the stymie permanently. The rest of the world kept it.

The USGA went it alone with the publication of the 1947 rules - a reorganisation rather than widespread change.

The R&A 1950 rules followed the same theme, and the previously separate match play and stroke play rules were combined, sections laid out more logically. Both these issues formed the basis of the first joint R&A and USGA code issued in 1952.

With the joint publication of the 1952 Rules, the issues of the stymie, centre-shafted putters, and lost/out of bounds/unplayable penalties were all reconciled. Match and stroke play rules were integrated.
The explanation cannot be more eloquently put than the statement by the two authorities in the preface to the 1952 edition:

PREFACE

This edition of the Rules of Golf is the result of a joint revision by the Royal and Ancient Golf Club of St. Andrews, Scotland, and the United States Golf Association.

For some years a growing desire for uniform Rules has manifested itself and this has now been achieved after special committee conferences in which representatives of Canada and Australia participated also.

It has been customary for both the Royal and Ancient and the United States Golf Association to revise their Rules periodically and individually in the light of experience. However, there has been no regular machinery for co-ordinating their respective views. As a result, differences have crept into the Rules. Departures from uniformity are no new phenomenon, for in the early days each prominent club in the United Kingdom had its own Rules. Nevertheless, as the game spread, it became recognised that uniformity would be advantageous to all, and towards the end of the last century, the Royal and Ancient Golf Club, as a result of requests from the main clubs in the British Isles, published the first uniform set of Rules.

The history of the present code dates to the end of the recent world war. The United States Golf Association had revised its Rules and the Royal and Ancient were in the process of doing the same. Because there had been intimations of a deep interest in standardisation of Rules, United States Golf Association representatives were invited to visit St. Andrews and conferences took place there in the Spring of 1951. In a most cordial atmosphere, the negotiating committees achieved agreement on this unified code which subsequently was ratified by the Executive Committee of the United States Golf Association, and by the membership of the Royal and Ancient.

The Main Aims. - At the conferences three primary considerations were kept to the fore:
First, the perspective was to be world-wide to meet the varying conditions under which the game is now played.
Second, to achieve this objective, there would clearly have to be "give and take" over items of differing importance to different countries.
Third, the negotiating representatives reminded themselves that, if legislation lags too far behind public opinion, the legislation loses effect.

These considerations account for some of the new code's unusual features reflected by both inclusions and omissions.

The Putter. - At the beginning of the century, there were no essential differences in the respective Rules of the Royal and Ancient and the United States Golf Association. The first major departure from uniformity occurred with the introduction of the Schenectady putter in the United States. This was not accepted by the Royal and Ancient as a traditional form of golf club, but play with this type of club continued in the United States. Now, after nearly fifty years, it is agreed that this type has become traditional and universal use will be permitted hereafter.

The Stymie. - There were only a few other divergences in the Rules of play up to the late 1930s, when the United States Golf Association experimentally introduced its variation of the stymie Rule. By giving relief when balls were within six inches of the hole or within six inches of each other, it did away with an unpopular feature - the unnegotiable stymie. This type of stymie often resulted from a missed putt on the part of the opponent. The American Rule survived its experimental stage and until now has been in effect in the United States, although it was not adopted in other countries. Some five years ago, the Royal and Ancient took a referendum on the stymie amongst the governing bodies of various countries. The result suggested a more or less equal division of opinion for retention, abolition, and two other alternatives; i.e., the United States version on the one hand and abolition of stymies laid by the opponent on the other. The latter alternative means almost total abolition, as relatively few stymies are laid by the player himself. With opinion so widely divided on the issue of the stymie, there seemed little chance of achieving uniformity in a world-wide code by retaining it or adopting either of the other alternatives. Abolition of the stymie was therefore recommended and adopted.

The Ball. - There has been and still remains a difference in the size of the ball. This matter has been regarded in a somewhat different light from that of the Rules of actual play. Playing conditions differ in many parts of the world, and the ruling bodies held to the opinion that the smaller British ball is no more suitable for play in the United States than the larger American ball is suitable for play in Great Britain. It is hoped that in the future it may be possible to find some basis for standardizing the ball. In the meanwhile, and in this code, the size of the British ball is specified as not less than 1.620 inches in diameter and that of the American ball as not less than 1.680 inches with weight coinciding at 1.620 ounces. To give playing equality in international team competition, the United States Golf Association has legalized the smaller ball for use in such contests in its country.

The Penalties. - On the introduction of the 1950 Royal and Ancient revised code, there arose another major difference when the Royal and Ancient, as an experiment, made changes in penalties. The United States Golf Association continued with substantially the traditional scale. The Royal and Ancient had taken a referendum as regards the penalties for out of bounds, unplayable ball and lost ball, and they accepted the majority view that the penalty for all these contingencies should be reduced from stroke and distance to distance only. Playing experience however, soon showed that the removal of the penalty stroke was not an adequate penalty. Consequently, the Royal and Ancient decided to return to the traditional penalties, and so were of one mind with the United States Golf Association when penalties for the uniform code came up for consideration.

Maintenance of Uniformity. - In framing this code, attention has been particularly directed to clarifying the Rules, consolidating them wherever possible, and rationalizing the headings so that reference is simplified.

There is one final point. A unified set of Rules having been achieved, it is recognised that it can only be kept uniform by mutual agreement not to alter it unilaterally. If questions of alteration arise, the Royal and Ancient and the United States Golf Association will consult with each other and with the governing bodies in other countries, and will use all possible means to ensure the maintenance of uniformity.

HAROLD GARDINER-HILL, Chairman, Rules of Golf Committee,
Royal and Ancient Golf Club of St. Andrews

ISAAC B. GRAINGER, Chairman, Rules of Golf Committee,
United States Golf Association

Despite the well-meaning paragraph at the end, changes between the codes did appear unilaterally.
The USGA experimented with a trial distance-only penalty in 1960 for a ball out of bounds. The R&A, having done the same ten years earlier and rejected it, did not go along with it.

The USGA restored the stroke and distance penalty in 1961, though allowing a local rule to modify S&D to a stroke penalty only; then tried again in 1964. Eventually, they, too, saw that it was not workable and returned to stroke and distance in 1968.

1984 saw a major reorganisation of the rule book, a more logical layout, improving readability and simplification as far as it goes. No major changes, just a few rule adjustments. This layout has been the basis for Rules books up to 2018.

2019 A revolutionary re-write of the rule book. Simplified language, moving away from the feeling of a legal document to a modern way of speaking.
It is, they say, easier to understand and is more consistent in application of Rules and penalties. Diagrams and examples are included.
The number of rules has been reduced to 24, although the rule book is signifcantly longer than before. However, the new rules layout has incorporated much of the 1000+ decisions within it, and the Decisions book is no more.