According to Garcia-Molina (this is from memory) a database is any permanent store of data where the data is retrievable.
This, to my mind, makes a notepad file a "database". The whole issue here is context and semantics!
A database can mean pretty much whatever the person who uses the word says!
To give you another example, I used to work for an airline. The word "flight" meant 3 different things depending on whether you were talking to engineers, flight crew or sales people.
1) to an engineer, a "flight" meant an aircraft taking off and landing (one "leg")
2) to flight crew, a "flight" meant out from base and back to base (two "legs" - aka a "return")
3) to sales, a "flight" meant a season (high/low) of "flights" over a six month period - obviously many "legs" (also known as a "rotation").
Database terminology is fraught with the same issues:
Does a database have to be relational? Clearly not, although some purists might argue otherwise.
Does it have SQL or not? Does that make it a database? Clearly there were databases prior to SQL and many current databases don't support it!
If you store a list of phone numbers in a notepad file on Google drive, is that a database? Clearly by some criteria it is - it's searchable, the data is retrievable and permanent!
My answer to your question is to be clear in your definitions before you start a detailled technical conversation - as an IT person in the airline who dealt with engineers, flight crew and sales, I always had to stop and ask them what they meant by "flight" and then gently nudge them towards the terms "leg", "return" or "rotation".
Do the same in your conversations about databases and you'll not go wrong - "Are we talking about SQL Server or MongoDB?" &c.