Are PS3 Game Trophies The Same For PS4 Versions?

I just beat Tomb Raider on PS3 (thank you PS+) and enjoyed it so much that I started thinking about buying the Definitive Edition for the PS4 I just picked up last week. So I was wondering if I play and beat the PS4 version will it count as a new set of trophies. I'm not a trophy whore/hunter, I'm just curious.

It's essentially the same game so I would think the trophies would carry over.

I've played both editions and they're separate trophy lists. The PS4 is the "definitive edition". But otherwise the trophies are identical. I thought you were referring to games that came out cross-generation. Kinda like when games are cross-buy on the PS3 and PSVita they've managed to make many share trophy lists (thank God!) and you wanted to know if they shared the same list between PS3 and PS4. If you had AC:IV or BF4 on PS3 and PS4 would they be separate lists?

Most games across multiple platforms, including the Vita, have identical trophy lists. But they're also separate in that you can earn all the trophies in the same game but from a different version again. There's one game I know of that actually unlocks all the trophies you earned in the other version upon starting it up.