Earlier quoted context omitted.
The difference is that the component project depends on Github. Bower is much more low-level and unopinionated. All you need is a Git path.
That's because without using GitHub, Bower's packages aren't namespaced. This was something discussed at length on the component spec github. It sure feels like Twitter is avoiding giving credit where credit is due. No links to the component.json spec or any mention of TJ Holowaychuk's component feels smarmy to me.
I looked at the source and found that the initial public commit contains 79 files.