I am assuming that you are asking about the three Republican presidents of the 1920s. I have edited your question accordingly.
There were certainly major similarities between these presidents. The most prominent of these was that all of them were generally pro-business. They were all opposed to the sorts of reforms that Progressivism had pushed.
However, they were very different, especially in personal terms. Harding, for example was something of a playboy. By contrast, Coolidge was known as "Silent Cal" and was a serious family man (though he did enjoy dressing up as an Indian, of all things, and having his picture taken).
Politically, Coolidge was the most laissez-faire of the three. Hoover, by contrast, felt that government and business should cooperate. Where Coolidge thought that government should stay out of the way of business, Hoover thought the two should work together to improve the nation.
These three presidents had common attitudes, but they were certainly not simple copies of one another.