Fair enough, the ArcGIS API for Python documentation is wanting at times. It isn't uncommon for the ArcGIS API for Python team to make up new terminology when existing ArcGIS REST API terminology already exists, which I think is a disservice because it creates a level of obfuscation between the ArcGIS API for Python and the ArcGIS REST API.
You have stumbled onto one of those situations; specifically, FeatureLayerCollection. The concept of a "feature layer collection" only exists in the ArcGIS API for Python. Looking at the definition of FeatureLayerCollection:
A FeatureLayerCollection is a collection of feature layers and tables, with the associated relationships among the entities.
In a web GIS, a feature layer collection is exposed as a feature service with multiple feature layers.
So, a "feature layer collection" is really just a feature service by a different name. Given the ArcGIS API for Python started as a wrapper for the ArcGIS REST API, and primary remains so today, it seems odd to create this new terminology. Can a FeatureLayerCollection really exist independent of web GIS?
In terms of unpacking the phrase, "hosted" is sort of a throw away term. Isn't every GIS service hosted in some way, shape, or form? I think "hosted" generally is applied to services in AGOL or on-premises Portal as opposed to stand-alone GIS Server, but I consider the term just chaff. As talked about above, "feature layer collection" is just a "feature service." So, "hosted feature layer collection services" equates to "feature service services."
