‘Next door’ is used in giving directions or location to mean that one building is adjacent to another. For example, you might say that you live next door to your uncle, or that the post office is next door to the courthouse.
‘Next store’ sounds almost identical ‘next door’ when in speaking, but it’s just a way of talking about stores in order. For example: “We did a lot of shopping today. We started at Big Bazaar. The next store was Shoppers Stop, and after that we went to Lifestyle.”