OpenStreetCam is actually a project by Telenav, not part of OSM per se. However, as Telenav built their business on top of OSM data and their staff are real OSM anoraks, it was envisioned as a way to contribute more data to OSM.

correct me if I'm wrong, but I also had the impression that the OpenStreetCam data was licensed in a way that is at least a lot better for the public than Google's totally restricted proprietary terms…

This is correct. The OpenStreetCam license is superior to that of both Google Street View and Mapillary.

The Mapillary situation seems complex. What's clear is that volunteers shouldn't be assisting Google get still further ahead of the more open alternatives.

In my opinion, volunteers shouldn't be assisting any effort that doesn't end up with their contributions available under a liberal open license.

As has been mentioned OSC is not "part of OSM", it's part of the OSM ecosystem.

There is also Mapillary, which is also part of the OSM ecosystem and is very similar to OSC.