"Fetch" means "go, get something, bring it back". It sounds fine to me, but I guess that's from my closer connection to UK English. It can sound a little condescending if not used carefully, as it's usually a command for dogs.

It's not formal, but it is old-fashioned. The word sounds outdated, even to the British ear. In everyday English 'fetch' is rarely used these days (other than as a command for dogs!).

I believe "fetch" is common in British English, but it sounds old-fashioned in American English.

I think it is a little old, maybe not so commonly used anymore, but still used. Formal, maybe just a little. . The game played with dogs would still be called "fetch". Throw the ball/stick. Dog fetches it. Then of course will not give it back.

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