Surprised that no one has responded to you. I'll take a shot at it. I only dance the American version, but my wife has danced Latin.
The major difference between Latin and American ChaCha is the method of doing "Cuban Motion", or hip motion. In American rhythm dances, Cuban Motion is achieved by bending the knee and moving your weight onto that leg. This weight change causes your hip to swivel towards the bent leg. In Latin, hip motion is achieved by straight leg movement. As far as steps go, I believe that the majority of steps are acceptable in both methods.
Now as far as counting goes, in both American and Latin ChaCha, the dance begins on the second beat. To get started, most beginners take a side step on the first beat and then go into the first step. So for example, the gentleman's part would be: side step with the left leg on beat one, back rock with the right leg on beat 2, forward rock with the left leg on beat 3, do a quick right left right on beat 4 and 1 (the "cha cha cha") to the side, forward rock with the left leg on beat 2, etc.
This method results in, what I believe is, the most common counting pattern of 2-3-4 and 1, where the 4 and 1 is the three step chachacha. OR, as some teachers teach the count as 1-2-3-4 and 1, to help the dancer start correctly.