Benefits of identifying as 501(c)(7) versus just regular non-profit?

United States/NYS here.

My understanding is that nonprofit corporations do not have to pay any federal or state taxes, only file a Form 990. My understanding is that a 501(c)(7) is a special tax-exemption classification from the IRS that is reserved for social clubs.

So if any of my understanding above is incorrect or misled, please begin by correcting me! But assuming its correct:

If you’re already a non-profit, why both ever requesting a 501(c)(7) status, even if you are a social club?!? It seems like there are more restrictions on what a 501c7 can do (to earn or keep its 501c7 designation), and if there aren’t any additional tax breaks for 501c7, why ever apply for it or identify as one?