When somebody asks me for a cleaning estimate, my first question is always which one they mean. They are genuinely different jobs.
A regular clean is maintenance. Floors, surfaces, kitchen, bathrooms, dusting, the things that need doing because a week has gone by. It assumes the place is basically in order and keeps it that way. Weekly or monthly, whatever suits you.
A deep clean is the one that gets underneath. Behind and under things. Inside the oven and the fridge rather than the front of them. Baseboards, door frames, the tops of things nobody looks at. Build-up in the bathroom that a wipe does not touch any more.
The honest rule of thumb: if nobody has done the underneath in a year or more, you want a deep clean first, then regular cleans keep it there. Starting with regular cleans on a place that needs a deep one just means paying for the same visit repeatedly and never quite getting on top of it.
Move-outs are always deep cleans. So are most first visits.
I do both, one-off or on a schedule. Tell me the situation honestly and I will tell you which one you need — including if that is the cheaper one.