Everyone is basically using the same emoji. Unicode defines the standard, giving a textual description for each one.

Apple, Google, Microsoft et al come up with their own images to represent each emoji in the standard. So the actual images vary.

The timid also varies, some of the emoji that Apple have added recently won't work on other platforms until those platforms update to implement the latest characters. It isn't always Apple who are ahead.

The vast majority of the characters will just work everywhere, but look a bit different everywhere.