OpenStreetMap itself has no notion of layers. It has a rather simple data model for geometries and completely freeform tagging (so for example there is no technical enforcement of how a road is labeled a road in the main database). Naturally there is quite a bit of effort to use tags with clear shared meanings, but none of that happens in the database, it's the people building the editors and doing the editing that choose what the tags mean.

Consumers of OSM data generally do perform a data extraction step where the freeform tags are grouped together and perhaps normalized to some extent. So at that point you sort of start to have layers, but different apps will use different systems and rules for that step, so the layers are coming from the app maker, not from OpenStreetMap itself.

OpenStreetMap is just a database. It has no concept of layers (except the `layers=` tag used for stacking order of objects e.g. bridges). Products which use OpenStreetMap data are free to apply whatever "layer" abstractions in their UIs they like.

For a visual comparison, you can look at http://sautter.com/map/