An instance of the software running as a service? A service.
The official Bitwarden service has a free and a more featureful paid tier.
Element offers paid hosting as a service with a limited free tier.
OSM isn’t software?
Mastodon and Lemmy are hosted and financed by individuals or organisations who usually choose to offer their service free of charge.
All of these are FOSS underneath but have very different costs. There is a difference between commercial for-profit services (BW, Element) and non-profit/public benefit ones (Lemmy, Mastodon) with the latter usually being free of charge.
There’s very little difference between a commercial FOSS application as a service and a commercial non-free software as a service.
For example, you could also buy Slack as a service as opposed to Element. In the end it’s a bill of $x/user/month. Nothing “free” about that other than the hosted software’s source code.