If you are using them as nouns, they mean the same thing. If you are using them as verbs, they have different meanings as shop would be to go to buy things, and store would be putting things away that you do not need to use.

Hi, They are synonyms. I think a store is mostly a little bigger than a shop. But I am not sure. I am not a native speaker. The thing with English is that it has two sources for words, one Germanic and one French. Hence there often are synonyms for words, with one coming from Latin or French which is mostly a little more snobby, and one coming from Old English, Germanic language. Store : Shortening of Old French estore (noun), estorer (verb), from Latin instaurare 'renew'; compare with restore. Shop : West Germanic origin; related to German Schopf 'porch' and English dialect shippon 'cattle shed'. Annoying. But every language has its downsides, in Korean, there are a lot of synonyms because of politeness levels, I remember.

As ever - and I'm sure that fellow Italki users are bored of hearing me say this - but this is yet another difference between British and American English. I don't think that Bora from Turkey deserved to get a 'dislike' for saying that a 'shop' is small, while a 'store' is large. In terms of British English, Bora is correct - this is how I would describe the difference between the two words. 'Shop' is the main word which we use to refer to a place where you go to buy something. We might use the word 'store' if it's in the name of the particular shop (eg 'The Phone Store') and we use the term 'department store' to describe a large shop with different departments (like Harrods, Macy's). Otherwise, in British contexts, 'store' suggests a place where you store things - as in 'storage' or 'store room'.

I think, the same two but "shop" small, "store" large

If you are referring to a place to buy things, then that is called a store, no matter its size. But a shop is generally a small store.