Breaking down 2D graphics

So I’ve gotten to the point in Macromedia Flash where I can now make games. My current goal is to make at least to my knowledge the first Flash wrestling game.

I want it to be similar to WWF Wrestlefest for Arcade/MAME but there is one thing that is hampering me.

How do I do animations which for every character it is the same? Like when someone gets slammed, they ALL look the same, same animation. When they perform the slam, its all the same.

Like if I want to do a bodyslam animation, I can either make an animation for each wrestler doing a bodyslam on every other wrestler (which will take about 16 years to animate with added moves) or the way I thought it goes is that you have character1 play an animation of him performing the bodyslam and character2 plays an animation of taking the bodyslam at the exact same time. It would be an illusion that he is actually doing the move.

Or is it something more to do with skins?

Can someone explain to me how the basic ‘grapple’ animations worked back in the day so I can save myself a lot of time?