The definition of an "alt coin" that I like is the one based off Satoshi's description on page 3 of the Bitcoin white paper:

I summarize this as: "Bitcoin is the longest chain composed (exclusively) of valid transactions."
With that definition, a coin is "not Bitcoin" if:
(a) it's based on a blockchain that doesn't begin from the Satoshi genesis block,
(b) the blockchain
does begin from the Satoshi genesis block but is not the longest chain composed of valid transactions.
With that definition, there have been times in the past when Bitcoin was "not Bitcoin".