'find' suggests you need to search for one. 'fetch' means go and get them, and bring them back.

Note that in American English, "fetch" sounds rather old-fashioned. We would normally say "I'll go get you a doctor."

Collins online dictionary fetch https://www.collinsdictionary.com/dictionary/english/fetch 1. verb If you fetch something or someone, you go and get them from the place where they are. Sylvia fetched a towel from the bathroom. [VERB noun] Fetch me a glass of water. [VERB noun noun] The caddie ran over to fetch something for him. [VERB noun + for]