Like others have said, in most games, including older games and indie games, there shouldn't be a difference. But for a few of those new AAA games, it will make a difference.
Infact it could be the difference between playable vs unplayable as some ps5 ports are HUGE vram hogs, even at low resolutions, and even with settings turned down. Probably a legacy of the ps5 having only vram (well actually not true they have 512mb of dram, but I think thats reserved for OS stuff), and then their pc port equivalents, putting stuff that could have gone into system memory into vram. Sometimes these games are patched over time to work better with 8gb cards, but thats not a guarantee, or its done lazily by simply flushing the buffer, which can lead to things like missing textures.
I'm playing ff16 right now, and they went and put a rtx 2080, an 8gb card on their recommended specs. I really wish they would have put at least a 12GB card there. The game gobbles up an insane amount of vram. Well its hard to say for sure since the reports vary so wildly. Some people on 4060s and 3060 tis tell me its runs fine. But many tell me it doesn't. Even people with 4080s complain of performance problems. Its hard to square all the contradictory reports out there. With my 4090 I can see vram go over 15GB. But I have 24gb, so whether this is smart caching of things for faster loading, or irresponsible use of resources, I can't really say.
Anyway, to get back on point, there will likely be times that 8gb causes you problems. However for old, indie, or even new but lighter AAA games it should be okay. I can for example maybe think of 10 games off the top of my head that would give you problems. If you do start bumping into the limit there are a few things you can do to mitigate the impact. 1) upscaling 2) reducing settings, most importantly, textures.
I really don't like to reccomend 8gb cards anymore though. I mean. My 1070 was 8gb. And I bought that in 2016. It wasn't even a high end card. It was like $350. If you would have asked before buying I really would have pushed to get the 16GB version (well, depending on your workload) but I suppose whats done is done. And that doesn't mean your card is useless, you still have tools to lower vram use if a game uses a lot of it. And depending on the games you play, it might not end up mattering. Really depends on the game.
Don't forget to use upscaling! Xess is actually quite good, if thats not avaliable, you'll have to do with fsr, but even that is getting better. GL.