do I or don't I double that L?

I'm having a real hard time figuring out what distinction, if any, is made by native speakers of English between the two spellings for modelling/modeling.

Is one British and the other English? if so, which is which?
Do they refer to different things? is modeling what fashion models do and modelling what scientists do?

The verb 'compel' gets an additional 'l' when derived (compelling and not compeling)
But the verb 'boil' doesn't (boiling and not boilling)

Does it have to do with how many syllables are in the root? It doesn't seem that way since:
Counsel becomes counseling and not counselling...

WTF? Are there any other -l ending words that have this dichotomy of spelling choice?

Either the internet is no help or my googling skills are becoming worthless in my old age. I'll be super embarrassed if it's something incredibly obvious that I'm too dumb to see...