"Let's go to a different store."
ちがう is the verb "to be different". When used in plain form like this, it functions as an adjective on みせ (shop). 行きます is to go, and ましょう makes it "let's go" instead.
So, in the past I've learned that adjectives end in な or い, and in fact if I look up ちがう in a dictionary it says it's a verb.
So... what's going on here? Can a verb sometimes modify a noun (a bit like 'a jumping frog' in English)? If so, under what circumstances? Can it work with any verb? Or just intransitive ones? Enlighten me.
No, only the dictionary form ちがう functions as an adjective.
ちがう みせ = a different store.
As a single word or placed at the beginning of a sentence as an independent clause it just means 'wrong' and denotes disagreement.
ちがい can function as a noun, however.
みせのちがい = The store's difference(s). / The difference (between) the stores.
ちがいは何でしょう？ = What's the difference?
ちがう = wrong; different; to differ
ちがい = difference
It should be accepted either way. お店 is a bit more prevalent and colloquial, but that is not to say that simply saying 店 is wrong or unused. The only time that it would be wrong to use 店 is when you want to show respect for the store that a person works at, owns, etc. Other than that, the お prefix is just a polite manner of speech.
If I put "ちがうに行きましょう" would that translate to.. "Let's go to a different one" ?
When you omit the noun which is being referenced you still need a placeholder. In this case の could be used. ちがうのに行きましょう. Other placeholders for 'one' in this usage can be やつ, もの, ところ, etc. These are not significantly shorter than みせ, so it would seem unnecessary and unnatural in Japanese to substitute in this example.
違うのが欲しい 'I want a different one'
違うものが欲しい " "
違うやつが欲しい " "
I had been getting "hoka" for "different" in these lessons and suddenly I'm getting "chigau" - anyone else see that too? Is "hoka" incorrect for these contexts?
Not really wrong given the context, but 'hoka' is 'other/another' while 'chigau' is 'different'.
It's the difference between 'Let's go to another store.' and 'Let's go to a different store.' The subtle difference is that a 'different store' more directly implies that the first store was somehow unsatisfactory.