Indeed. The OED etymologies of the two different concepts are worth reading:
Etymology: In 17th cent. tap-too, < Dutch taptoe in same sense; < tap the tap (of a cask), + toe = doe toe ‘shut’. So Swedish tapto, Spanish (1706) tatu. Compare German zapfenstreich, Low German tappenslag, Danish tappenstreg, with the first element the same, and second element meaning ‘stroke, beat’.
Although Dutch tap toe was in military use in our sense 1 in the 17th cent., there is reason to doubt if this was its original use. Tap toe = doe den tap toe ‘put the tap to’, ‘close or turn off the tap’, was apparently already in colloquial use for ‘shut up! stop! cease!’; Dr. Kluyver points out, in a play of 1639 from Emden, Doch hier de tap van toe = ‘but here we shut up’, or ‘say no more’.
Etymology: In 18th cent. tattaow, tattow/taˈtaʊ/, < Polynesian (Tahitian, Samoan, Tongan, etc.) ˈtatau (in Marquesan ˈtatu) noun denoting the markings. (For the verb the expression is ta ˈtatau to strike or stamp tattoo.)
The word is recorded from Tahiti as tataou in Bougainville's Voyage autour du Monde 1766–9 (Paris 1771), and as tattow in Capt. Cook's First Voyage July 1769. The current English tattoo and French tatou are alterations of the Polynesian word.