Difference between .db and .sqlite file
Absolutely none. SQLite does not care the least what extension the file uses. It checks whether what it was given is indeed a SQLite3 database by inspecting the magic number and the header.
It's purely up to you whether you use the suffix .db, .sqlite, .dat, .mydata, .foo or whatever... or no extension at all; that is also permitted. There is no standard and the documentation does not seem to make any particular suggestion either, so everybody uses something else.
Also, if you are using SQLite as a storage backend for your application, it actually makes sense to use extension specific to your application. Because it is not just any random SQLite database, it is SQLite database with specific schema storing particular kind of data.