Confession; former competitive tennis player with a substandard serve (actually better after I stopped playing seriously/teaching). The differences in surfaces are magnified as the level of tennis gets better. Grass, if well maintained, is not too tough at lower speeds. However the ball tends to skid on powerful shots making it a very fast game.
There is a major difference between har tru/rubico courts and common red clay found in Europe with Italian clay even slower than that found in France. Part of this depends on the amount of top surface. If a club puts down too much har tru it slows the court down. Also the europeans used to play with balls with less compression (save the obvous wisecracks please). In the old days, the combination of slow courts and "soft balls" essentially removed the serve from the game and made approaching the net very difficult.
Hard courts vary with the construction. For example, the tennis center in Kalamazoo where the National Juniors were always played was quite slick with lower skidding bounces than you find at places like Flushing Meadows. However they all have very true bounces.
Notwithstanding these differences, they do not compare in architectural diversity with golf courses. The dimensions are always the same.
The biggest differences in the evolution of the game has been caused by equipment. The larger headed better balanced rackets have allowed players to use Western forehand grips and the two handed backhand to hit tremendous topspin ground strokes and serve returns that were impossible for all but a few (e.g. Laver using mostly a continental and sometimes eastern grip). Combined with the increased serve speed (again exceptions e.g. Gonzales, Tanner, Sangster etc) makes it almost impossible to get to net behind serve even on grass. A server like Federer would have followed his serve all the time. (see Talbert and Olds; The Game of Singles in Tennis, a brilliant but sadly outmoded study of tennis tactics) This has led to tactics closer to those used by Kramer in the late 40's than those used by Laver in the late 60's being prevalent.
I'm not sure which I like better, but Laver hitting with rackets of this type would have been something to see. The vaunted rpms on Nadal's groundstrokes would have been in serious danger.