やんちゃ is used for both boys and girls and emphasizes mischievous, naughty behavior, while おてんば is specifically for girls and focuses on boyish, active traits.
活発 is a more formal, gender-neutral adjective meaning 'active' or 'lively', without the boyish connotation of おてんば.
Etymology
The origin is uncertain. It may be related to お転婆 (otenba), where the kanji 転 means 'rolling' or 'tumbling' and 婆 means 'old woman', but the exact derivation is unclear. The word is now used exclusively for tomboyish girls.