- the schema of the map: what objects are available in each tile at different zoom levels. It sounds like versatiles uses the shortbread schema (contrast vs OpenMapTiles, protomaps)
- a container format: a way to pack multiple tiles into a single file. It sounds like they created their own format here (contrast vs mbtiles, pmtiles).
- the scripts/tooling to build everything
- the overall finished map product itself (contrast vs Google Maps, Stadio Maps, protomaps, OpenMapTiles, etc)
The versatile container format seems to require a custom HTTP server. But if you want, you could produce the versatiles map and store it in a pmtiles container. Or you could stick a caching proxy in front of their publicly available tile server at https://tiles.versatiles.org/tiles/osm/{z}/{x}/{y}
It would be interesting to hear them describe why they decided to create their own container format. The text that I have found seems to be contrasting it to RDBMS containers, but is silent about mbtiles/pmtiles.