No. The remote data can use any kind of SQL database (SQLite or otherwise), or does not need to use SQL at all (and even if it does use SQL, the view does not necessarily have to resemble at all the actual schema that the server uses to store the data). It does not even have to be stored data; it can generate the data on demand if needed. It is not direct database access! You have public access to the data, as the server implements it.
A few examples may be possible to specify. I mentioned above movie showtimes and weather; even if they come from different services, you can make a joined query on the client side, such as to find all movies playing within ten miles in places that are not raining, or whatever. Another use is you might hvae some set ofdata that occasionally gets updated (e.g. Magic: the Gathering cards Oracle texts), and you might make a local backup with incremental updates (which will be efficient if there is a last updated column, and the server can use such a constraint in the WHERE clause (if the server doesn't support the constraint, the client will interpret it and download all data and filter it), so that you need not download the data that you already have). Another example is remote databases that many people can help to add the data to (it can be writable too and need not be read only).
It isn't another version of SQLite; you can still use it with the ordinary SQLite (or implement the protocol even outside of SQLite; this protocol does not use any SQL codes, so it does not need to be used only with SQL, although it is designed mainly for use with SQL).