Can 「屋」and 「店」be used interchangeably when describing a store? For example, 「文房具屋」 vs 「文房具店」？ Is there a difference?

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I think you can use them as interchangeable words in most cases, like 文房具屋＝文房具店, かばん屋＝かばん店.
Basically, people tend to use 屋 for stores that have existed for quite a long time, stores that have rich histories, or small stores that sell particular types of ingredients/items like family-run stores. 店 is relatively used for new types of industry/stores that have fewer histories, chain stores, or bigger stores. Still, the usage would depend on the person or the word in many cases because the way to choose is kind of vague.