Many people may be wondering that what’s difference the wording between “Elevator” and “Lift”?
Actually, both of these words mean "elevator" (passenger). Their meaning are the same but the word
ELEVATOR [n.] is an American English term
LIFT [n.] is a British English term
Sometimes, if you say lift it might sound like lip, which means lip which can be confusing.
So it can be used both because they are same meaning up to your choosing in the appropriate situation.