I'd say claws for nails is not in typical casual conversation. But it can be used to convey anger, aggressiveness, or being attacked. Also, I'd say it has a feminine connotation, but it need not be strictly feminine. Examples:
He's so hen pecked (nagged) that he has claw marks. (this is metaphorical and there need not be physical. if there is physical abuse, it could be a partner scratching and injuring their partner, but I'd say more often it is a metaphor).
You can take your claws out of me. I don't feel them anymore. Nice try. (man to a woman, you can stop verbally abusing me, I don't feel it anymore and I don't care anymore).
Let's claw into this problem! (let's attack this problem with intensity).
In common speech, if you call someone's nails claws, it may also be construed as ugly. Other comments about claws below are good. These are just some examples. Sometimes with friends, as described below, it can indicate familiarity, but unless you know the English language and friends well, I'd be careful with that one, especially as a man to a woman.
"Paws" also implies animal behaviors. For instance, "He pawed all over her on that date" can have a sexually aggressive date and if recited by a woman to decide an unwanted advance, it can have a very negative connotation. Sometimes, as described below with female friends, it can be endearing. Mom to kids: OK, kiddies, show me your paws.
I am from the middle states and south of the Ohio River. Some of what I talk about may be a bit southern USA dialect, but I'd say this would be true no matter where in the USA you are.
Best wishes to you and your studies. I hope it helps.