The verb 引く gives 引き出し ('drawer'), which is a straightforward etymology shared by Japanese and English (and French and probably more). But 引き分け seems to also have an etymology similar to 'draw' (as 'tie' in sports) in English; and this etymology is not so self-evident. Is there a shared logic, is it a coincidence, was the word imported and translated?
引き出し is 引き "pulling" + 出し "coming out". By extension, "that which pulls and comes out" or "that which is pulled and comes out": a drawer.
- Technically speaking, the Japanese term does not share its etymology with any other known word in another language: etymology refers to the specific derivation of a word and its constituent parts. Neither English nor French have any words even remotely related to 引き出し (aside from any borrowings from Japanese). The word-formation process in the three languages might be vaguely analogous, which I think is what you mean.
引き分け is 引き "pulling" + 分け "splitting, dividing". By extension, "that which pulls and divides", or "that which is pulled and divided".
- In the absence of any specific number, this often refers to splitting something in two halves, and that sense in the context of a competition yields the idea of the two teams being equally matched: a tie, with neither winning and neither losing.