In visual studio, I can do a code review for someone and add comments to their code... In their instance of visual studio they can see those comments. All good so far.
But if you go to Team Foundation Server (TFS) Online, you can't see those comments at all. And if you make code comments in the tfs online web interface, those comments are not seen in visual studio.
I thought I would be able to see all comments across both visual studio and in TFS Online but it doesn't seem to work that way.
Is there a setting I'm missing, am I misunderstanding the functionality, or is this unimplemented?
Code Reviews and Lightweight code commenting are two complementing features, but also unrelated features. Yes they both allow you to comment on code, but as you've found out, the data between these two is not shared.
There isn't much you can do right now, except for going to the Visual Studio User Voice and explain what you'd love to see (or search for an existing suggestion and add your votes there).