So when you parry in this game you have the option to perform a counterattack. I already know that. But sometimes, there are these different animations, but I don’t know how to trigger them. These animations are NOT counterattacks. I am sure of it.
I appreciate all comments!
Do you mean things like the kick, and other strikes post parry?
I’m really not sure 
…I’ve got it in my mind that there’s only one particular counterattack animation / movement in the beta
Maybe you accidentally launched some combo? Combo list is in your stat page 
There is something called “perfect parry” in the game.
This is triggered when you have perfect timing with your block.
Perfect parry is a special animation like: pommel bash, pushing through your opponent and many more.
Perhaps that is what you saw.
