I use Git on a daily basis, but I never understood it.
If I just want to commit a specific part of my changes, I just do it. It's nice to see which files are staged for a commit, but I also see them in the commit msg comments.
They're called "hunks" in git parlance: sections of the file that define a "diff". A diff on a file can be made of multiple hunks.
Very often, my changes to a file are a mix of "fixing a serious bug" and "minor refactoring" and "removing dead code". When the time to commit comes, git makes it trivial to separate all these changes in different commits so that each commit does one thing and one thing only.
I just noticed recently that TortoiseHG lets you do that in the GUI. Definitely is a nice feature. I only just started using Git and did like the ability to cherry pick from a file, but happy to know I can still do that with hg.
Actually Hg record can do this. It lets you 'edit' a hunk using a text editor, before adding it to the list of changes to include in the current commit....
This is probably more a symptom of the fact that either your workflow doesn't require an index or you don't understand its value.
Either way, the index is by far git's more popular and used feature, besides branches.