Essentially, Fonline is the engine, which is fan-made and open-source.
The Engine was made for the first (fan made) Fallout MMORPG (TLA if i am not wrong), but it could be used and is indeed used for other kind of MMORPG & solo games, not necessary Fallout related.
It features many improvements over the Fallout engine, like 3D models compatibility, choice between TB & RT, bigger maps (most fallout cities now have a single map), the ability to un-zoom widely, keyboard binding etc...
Currently there must be 5-10 Fallout MMORPG servers with their own gameworld, their own custom maps, their own rules. What could be said about one server could be wrong about another as they only share an engine and some modding tools. I know there is also a game set in feudal japan, with customs graphics (impressive ones)
Hexer's Van Buren project use the engine for a solo game.
As for Fonline2238, it included the whole Fo1-Fo2, and a lot of custom locations.
It was supposed to take place between Fo1-Fo2, with all the south conquered by NCR, got character from both games, for convenience, but different quests & dialogs.
Essentially, it is an MMO. Even if you could do many thing alone, most player end up in gangs, as gangs can take control of cities, to get reward.
When you controlled a town, you got access to a militia and enforce your law.
Some used that to enforce safe trade or roleplay project, some used that to tax the players who came to trade with npc, but most used their militia to free kill any new comer.
I am currently trying Ashes of Phoenix, that is made by some of my game mates, but i try to avoid spending too much time in it.
I don't know much about other servers.
About number of players by server, it range between 5 & 500 players depending on the server, the season and the hour.
I think the fonline 2238 playerbase was like 100-300.