書店 is the written word for 本屋, and 書店 is basically used for shops' names. For example, A: 〇〇書店にはたくさんの本がありますね。 B: はい、だから私はよくあの本屋に行きます。

Really interesting question！ As На добраніч-san explained, that is one of the differences. Other differences are like these in general; 書店 is formal VS 本屋 is casual. 書店 is large or chain store VS 本屋 is comeratively small . (Everyone knows the name chain store name; that's why name of store could be used in the case of 書店. ) 書店 has variety types of books VS 本屋 has treatises. As FYI, ～屋 could be used for the store privately owned and specialize something. ex. Store for fresh vegitables：野菜屋 Store for sweets: お菓子屋 It sometimes sounds a bit old, but you can use like these. Hope it would somehow help for you😄