It seems they are etymologically related too. From ONLINE ETYMOLOGY DICTIONARY:

violin - 1579, from It. violino, dim. of viola (see viola).

viola - 1797, from It. viola, from O.Prov. viola, from M.L. vitula "stringed instrument," perhaps from Vitula, Roman goddess of joy (see fiddle).

fiddle (n.) - O.E. fiðele, probably from M.L. vitula "stringed instrument," perhaps related to L. vitularia "celebrate joyfully," from Vitula, Roman goddess of joy and victory, who probably, like her name, originated among the Sabines. The word has been relegated to colloquial usage by its more proper cousin, violin, a process encouraged by phraseology such as fiddlesticks (originally "the bow of a fiddle," meaning "nonsense" is from 1600) and fiddle-faddle, which is unrelated, being a reduplication of obsolete faddle "to trifle."

~Masato