Family Share is when multiple family members, each with their own account, collectively combine and share their libraries with everyone within the Family Group.
https://steamhost.cn/help_steampowered_com/en/faqs/view/054C-3167-DD7F-49D4

Remote Play is when you stream a game from one PC to another device. Inputs into the second device get sent to the PC, and as the PC renders the game it sends the video to your other device.
https://steamhost.cn/help_steampowered_com/en/faqs/view/0689-74B8-92AC-10F2

You could conceivably use both in your scenario depending on your own use-case. I don't have an personal experience how the two work together, but that's what each option provides.

So if no one else has a steam account yet, no real purpose in them making one? Sounds like the idea would be if two people had separate libraries, they could share them, but if there is only one library, no reason to make other accounts, as there is nothing to share?

Would there be any instance where someone in my family might be able to play on their phone with someone on the pc? Or two people could play on their phone without the pc at all?

Neither are required if you play split screen games on the TV, Then you just have to browse the steam store to find the relevant games that offer split screen compatibility, Then the whole family can enjoy playing games together on the TV with the controllers.

Go to steam store, Click on the magnifying glass in the search bar, and Filter Narrow by number of players

Shared/Split Screen PvP
Shared/Split Screen Co-op
Shared/Split Screen

There are thousands of popular games that support it.

Originally posted by KaveMan:

Neither are required if you play split screen games on the TV, Then you just have to browse the steam store to find the relevant games that offer split screen compatibility, Then the whole family can enjoy playing games together on the TV.

That's what I'm going for first. Maybe I'll try to get that going and then come back to these if it feels like we are missing something. Thanks!

Thought i will admit, steam advanced search does not correctly list couch co-op games that supports 2-4 players, it sometimes requires a bit of digging around.

Example

https://steamhost.cn/app/355050/Sky_Force_Anniversary/

supports up to 2 players local co-op but does not have the tags listed properly.

https://steamhost.cn/app/396900/GRIP_Combat_Racing/

Supports up to 4 players split screen

Hope you find other games too that you might enjoy with the family!

Originally posted by KaveMan:

Thought i will admit, steam advanced search does not correctly list couch co-op games that supports 2-4 players, it sometimes requires a bit of digging around.

Example

https://steamhost.cn/app/355050/Sky_Force_Anniversary/

supports up to 2 players local co-op but does not have the tags listed properly.

https://steamhost.cn/app/396900/GRIP_Combat_Racing/

Supports up to 4 players split screen

Hope you find other games too that you might enjoy with the family!

Thanks for this! I purchased Overcooked 2, Stardew Valley, and It Takes Two. Purchased a few Myst like games for my wife who likes that kind of game. I'll check these two out too. Four player racing sounds fun.