People who aren't familiar with diving, probably refer to ANY kind of diving in the ocean as "deep sea diving".. If a diver were to use the term, it might refer to dives that are deeper than 130 feet, which is the depth you are certified to dive to in an Advance Open Water Diving certification..
I think, for the most part, it just refers to diving in the ocean at any depth.. I think that term was coined when diving was first invented.. At that time, going past 20 feet deep in the ocean was probably considered deep because you were limited to the depth you could go while holding your breath - even tho I know back in the day some locals in remote islands could dive to 300 feet deep on a single breath to go get pearls and stuff..
The deepest I've ever dove was 137 feet.. I prefer shallower dives - in the 40-50 foot range.. you can stay down much longer and things are lit up more by the sun.. plus you don't run into as much trouble with decompression issues - although you still can.. its just not as easy as at much deeper depths..
Friendship is like peeing your pants.. Everybody can see it, but only you can feel the warmth..