the hardest thing in that genre discussion is that ambient and dub were born in 1970 much earlier than other 'relax' genres, and if we are talking about, for example, The Infinity Project - Mystical Experiences, that was released in 1995, we need to know, that trip-hop was born in 1993-1994, downtempo in 1995-1996, and chill-out even was a slang word.
On the festivals we usually have two stages: psytrance and chillout. With my friends we don't usually use neither psychill nor psybient. We say "chill music" or "chillout" and only throw in "ambient" if something's really slow (most of the time beatless but with few exceptions) but it's equally descriptive as "dub", "oriental" or "bass". So yeah, for me, psybient is de facto a sub-genre of psychill music. And that's how it goes around in the world, with few exceptions, of course. I haven't met a DJ that focuses solely on strictly beatless and ambient music but some of us do play ambient sets once in a while.