As verbs stay and live have one important difference.
If you stay somewhere it means that you are there only temporarily.
If you live somewhere it means that you are there permanently as a resident.
- I have been staying in Barcelona for three months.
(I have a plan to leave.) - We stayed for three nights in a wonderful hotel.
- I have been living in Barcelona for three months.
(I have no plan to leave.) - We lived there for more than 10 years.
