Difference between "Where are you living?" and "Where do you live?"

The difference is in the mind of the speaker. If the speaker conceptualises the question as referring to a temporary state (living in a particular place) or a repeated action over a limited period (travelling), then the continuous form is more likely.

So, if my friend moves to San Francisco on a two-year contract, I am more likely to ask her a couple of weeks later: Where are you living? than Where do you live?

Similarly, if I want to know if a new acquaintance frequently travels on business or vacation, I ask: Do you travel a lot? But, I would be more likely to ask my San Francisco friend a few months after she's started her temporary contract: Are you travelling a lot?


It is worth quoting at length from Lewis in The English Verb (pages 85-87) for a better understanding of the reasons that native speakers choose one or other of the two forms exemplified in this question:

We need to remember that this form (the present continuous/progressive) is not technically a tense, but an aspect. Aspects give the speaker's temporal interpretation of the event. They do not refer to real time, but to psychological time - to the speaker's perception of the temporal quality of the event.

...

We need to contrast: I live in Oxford and I'm living in Oxford.

...

We need to remember that the speaker's choice of verb form conveys both the fact, and his or her attitude to, or interpretation of, those facts. The question is not whether my living in Oxford is a period of time but whether, at the moment of speaking on a particular occasion, I wish to emphasise that it is something which will occur for a limited period of time.

With I'm living in Oxford, the speaker conceptualises a temporary state; in psychological time the period is limited. This limit is not suggested by I live in Oxford.