both armies; both forces
Refers to two opposing military forces or armies in a conflict.
両軍は激しく戦った。
Both armies fought fiercely.
Both teams will face off in the final match.
both teams; both sides
Extended to sports, games, debates, or any competitive context with two opposing sides.
両軍の選手が握手を交わした。
Players from both teams shook hands.
国境付近で両軍が激突した。
Both armies clashed near the border.
Players from both teams shook hands.
Both sides were evenly matched in ability.
双方 is a formal, neutral way to say 'both sides' (often in negotiations or legal contexts), whereas 両軍 is specific to military forces or sports teams.
両国 means 'both countries', while 両軍 means 'both armies/teams'—learners may confuse them because of the similar 両＋noun structure.
Compound of 両 (both) and 軍 (army, forces). The extension to non-military contexts is a natural semantic broadening.