Seems like there are at least a couple of things that can be unlocked online if you finish single player. Where is the whole list?
There is nothing like this that exists in GTA Online.
The only thing you could potentially be thinking about is the GTA Online Story Mode, which takes your GTA Online character through a scripted Story Mode in which you will interact with the characters from the Single Player Story.
Besides this and some other characters doing a crossover between Single Player and Online, they do not affect each other in any way.
GTA Online includes its own Story Mode. Taking place months before the events of GTA 5 single-player, the story takes the player's Character through series of Missions and encounters with GTA 5 characters.