OK, you're talking about John Austin's Speech Acts theory.
To be a performative utterance, there needs to be proper felicity conditions.
Felicity conditions - Wikipedia, the free encyclopedia
Austin's Felicity Conditions
A - There must be a conventional procedure and the circumstances & participants in the procedure must be correct
B - The procedure must be fulfilled correctly and completely
C - In certain cases, the person must have the correct though, feelings or intentions; if consequential action is required, these actions must be performed
"I now pronounce you many and wife", is only a performative utterance (a valid utterance performing a marriage) if the following felicity conditions exist:
- The utterer is legally entitled to perform marriages
- The couple being married intend it to be a serious act
etc.
So, i) there is no "difference between a felicity sentence and a performative one", and
ii) very few of these linguistics definitions that you are learning exist independent of the name of a linguist who has invented them. It's only when they are widely known that you can ask "What maxim does this sentence violate?" and expect someone to know you are talking about Grice's, for example. Same for Austin