I've never heard of this disambiguation. An unlocked cellphone has always meant (1). A rooted or jailbroken phone means (2). For three, why would it make sense for manufactures to advertise a phone with/without a lock screen? It doesn't make sense.
Is that really something that gets confused often or any more often than any other disambiguation in the English language?
fastboot flashing unlock_critical
So it seems that at least in some contexts, "unlock" can refer to the bootloader (sense 2 above).Also I wasn't as clear as I intended to be with sense 3 above - it might also mean temporarily screen-unlocked, as in "can you please unlock your phone so I can enter my number?".