Topic: 2player definitions

Total newbie here. Apologize up front for the elementary questions. Off these answers are already here, please direct me to the appropriate threads.

Just purchased a PS4. Exclusive for the purpose of bonding with my wife. My questions revolve around 2 player terminology.

For starters, I know that there are two types of "local" 2 player games, ones with split screens, and ones where you both play together on the same screen. My initial question is when shopping for games is there a way to tell the difference between these? It seems simply being marked "2 player" doesn't provide this ability.

Secondly, I have noticed that when reading articles about "best 2 player games", they talk about "local" vs "online". From what I gather, talking about 2 player games while playing online is referring to 2 or more people playing, but at different locations. So this isn't really what I'm after either. So am I correct in presuming any multiplayer games that are only online games are not what I'm looking for?

Lastly, can anybody recommend games that are 2 player games, preferably where you work together, that would be fun for two people, located in the same room, using the same system and not split screen? Am I correct in feeling like there are very limited games like this?

Thanks for any help and sorry again for the lack of basic knowledge.

@Hiriqnu Yeah - exactly as @stuzster said pretty much.

In terms of reviews and recommendations online, you'll be looking for local co-op or couch co-op as it is commonly referred.

Good examples of favourite couch co-op games are things like 'Overcooked' or 'Moving Out' which are quite fun to play together. As you say, some are all on one screen and some are split screen but they'll probably fall under the same couch co op description.

@Hiriqnu I'm a big fan of a game called Lovers in a Dangerous Spacetime. It's a space exploration game, kind of. Check it out, it's great fun in two player