More like "single process application's database".
There are interesting use cases for DB-per-user which can be server or client side, or litestream's continuous backup/sync that can extend it beyond this use case a bit too.
You _can_ use SQLite as your service's sole database, if you vertically scale it up and the load isn't too much. It'll handle a reasonable amount of traffic. Once you hit that ceiling though, you'll have to rethink your architecture, and undergo some kind of migration.
The common argument for SQLite is deferring complexity of hosting until you've actually reached the type of load you have to use a more complex stack for.