Live Share is different than other collaboration tools in that it supports Language Features and Collaborative Debugging. By Language Features I mean all participants get auto completion, go to definition, error checking etc. Collaborative Debugging allows multiple people to step through code, inspect variables or look at call stacks.

I don't know why the GitHub doc get linked, but this page probably gives more context: https://code.visualstudio.com/visual-studio-live-share

Disclaimer: I work at VS Code and have tried Live Share in private preview. Honest feeling is it still has some gaps, but if everything would work out of the box it can be pretty awesome.