職人 is a broader term for a skilled worker or artisan, while 手工業者 emphasizes handcrafting and small-scale production.
工芸家 often implies an artistic or design-oriented craftsperson, whereas 手工業者 focuses on the manual trade aspect.
Compound of 手工業 (handicraft industry) + 者 (person). The exact historical derivation is uncertain, but the word follows a common pattern for occupational nouns.