I have noticed a few times people saying "<x> is not a fast". In fact, I have said it myself in reference to Michael Mosley's approach.
So I thought I would check out what fasting is in the English language, and my favourite source of that is the OED. Above our the screenshots of all their definitions (ok, one is missing because I didn't understand it)
It ties in with my early understanding. My parents used to practice religious fasts that consisted of 3 meals but no snacking in between. So yes, fasting covers a wide range of self-denial, not just the complete absence of nutrition.
(love the Irish tradition of fasting against. Sitting on the doorstep of someone that owes you money, refusing to eat: oh, yes, I could imagine my Irish ancestors doing that)