[6string]

Please correct me if I'm wrong but this has been my
understanding

Up the fretboard is towards the sound hole
Down the fretboard is towards the head stock

high and low refer to pitch
top and bottom refer to actual physical position

the low E string is the lowest in pitch the one above the A string,closest to the ceiling.
the high E string is the one under the B string,closest to the floor.

but the bottom string is the one closest to the floor
and the top is the one closest to the ceiling.

I've seen videos where people described themselves as

"I am a pro Guitar Player/Teacher." saying the bottom
strings are the bass strings.