I have heard English speakers say 'take off' about leaving (starting to move) on a motorcycle sometimes. It's interesting to me that the expression which is used when an airplane is leaving the ground is used for motorcycle too. But I'm not sure if the same expression can be used for cars (four-wheel automobiles). Do native English speakers say 'take off' in a sense of 'begin to drive a car'?
We sometimes use take off in the sense of leave, without specific reference to the means of transport. I hadn't realised the connection to air travel until you mentioned it---they may be historically related, they may not be.
You could certainly imagine your friends who are about to leave your dinner party and walk home saying:
- We're going to take off, I think; thanks for a lovely evening.
This makes it clear that there is no necessary link to a certain means of transport.
(And, by extension, you could also use it if you were about to drive home by car.)