see the
Database citation at
Dictionary.com | Find the Meanings and Definitions of Words at Dictionary.com for the formal definition.
I'm working from a very old (circa 1978) and mostly unused memory, but I think it was from either
CACM or an IBM Fellowship Paper that I read the first formal definition of database. The reference was about the switch from physical media (tape or punched cards) to the concept of "online data" and the need to form a "Data base" from which to build applications. The gist of the definition was that data formed the base on which all programming was built, and that having a "data base" would allow applicaitons to be developed faster and easier than ever before. Unfortunately, I can't give you an exact citation... Too many years have passed for my feeble brain to retain that level of detail.
Yes, a database is a collection of zero or more files. Depending on how the database engine manages its persistance, there can be no file at all or there can be multiple files per database entity (such as a SQL table) and almost everything in between.
A single file from a multiple file database may or may not be able to stand alone. I can only think of one case where it could be considered a database on its own.
Professionsals working in information technology don't call spreadsheets databases. Users sometimes do.
-PatP