Sometimes when watching youtube I’ll come across videos like “cool Phrygian lick”, and the “lick” is like 27 notes long and what I’d class as a Run rather than a Lick.
Would you say thats right or wrong?
It’s something I’ve seen a lot and perhaps my concept of a lick is wrong.
What number of notes do you think is the rough cut off point for classing it as a lick?
It’s more contextual I would say and if I were to describe it, It’s not the number of notes per se it’s more the phrasing. A run I would classify as a line played fast (thus the term run) that connects two things, it could be another phrase or the ending note. A lick is something that is just a phrased idea, and can be anything, nor does it have to be fast. Either can be long or short.
Yes also for me a run is something that builds energy towards some kind of end point/climax or a transition in a song or solo. In my mind it is similar to a drum fill.
(I have no idea about official nomenclature)
This is not official at all, but in my own mind licks go ‘nowhere’ and runs go ‘somewhere’. I don’t enjoy licks. I’m in the minority, I know. Freebird is one of the most beloved solos of all time and I can’t stand it. It’s all ‘licks’ to me. Just a pattern of 3 or 4 notes, over and over again. Then it changes to some other pattern of 3 or 4 notes, over and over again. Now, the opening ‘theme’ in that solo I think is cool :-). And again, I’m not trying to offend. I think there is nothing wrong with enjoying that solo, and if anyone enjoys it, I am happy for them 
Runs I think of more like a jazz line. It has a clear melodic contour. Jazz lines are always going ‘somewhere’. That’s why they are called lines! A line that goes nowhere is a…circle haha!
I hear the term ‘runs’ a lot in the context of bluegrass music (fiddle and guitar). Those are almost always melodies.
I think to many though, the terms are interchangeable. Just some ‘collection of notes’ that have a certain identity.