mid-14c., in reference to some part of a harness;" c. 1500 as "act of pulling or dragging," from tug (v.). Meaning "small, powerful vessel for towing other vessels" is recorded from 1817. Phrase tug of war (1670s) was originally figurative, "the decisive contest, the real struggle," from the noun in the sense "supreme effort, strenuous contest of forces" (1650s). As an actual athletic event, from 1876.
"small open vessel (smaller than a ship) used to cross waters, propelled by oars, a sail, or (later) an engine," Old English bat, from Proto-Germanic *bait- (source also of Old Norse batr, Dutch boot, German Boot), possibly from PIE root *bheid- "to split," if the notion is of making a boat by hollowing out a tree trunk or from split planking. Or it may be an extension of the name for some part of a ship.
French bateau "boat" is from Old English or Norse. Spanish batel, Italian battello, Medieval Latin batellus likewise probably are from Germanic. Of serving vessels resembling a boat, by 1680s. The image of being in the same boat "subject to similar challenges and difficulties" is by 1580s; to rock the boat "disturb stability" is from 1914.
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Definitions of tugboat from WordNet
a powerful small boat designed to pull or push larger ships;