That's right. Fdroid the app is just a program that accesses repositories. It's not even the only one, Aurora has a similar version of their own called Aurora Droid.
Fdroid the repo is a repository of FOSS apps maintained by the Fdroid team with apps they've reviewed and compiled themselves, to provide an element of trust that you might not get from every random developer.
There's no fool proof way of handling app trust other than developing your own understanding of the code. Otherwise you have to trust someone. Fdroid seem pretty trustworthy, more than the big corporations, and more than many unknown small time developers - however you can get app updates quicker direct from the developer, through the Fdroid app, if you're willing to trust them.