1. Unless a client loads all of the reactions to all the posts you see, it can't know whether or not you've already liked it. NostrGram checks this and indicates you've already reacted to a note by making the heart a solid red. It can do this because it uses a caching server that makes it very fast to do so.

2. If the client you're using doesn't check whether or not you've already reacted to a note, it can (and will) write multiple reactions to the same note for your pubkey, and there's nothing in the relay servers that prevents this. NostrGram checks if you've already reacted to a note and doesn't let you do so again.

So yes, it's very client-dependent how the social engagement is handled.