Thanks for clearing that up. But which came first, battle (the formation) or battle (the scrap)? It's the chicken and the egg all over again...
Right, I am definitely not an expert, but looking at the word origin, I'd suggest that the formation came first and then morphed into the scrap after the medieval period - as the battle terms seems to stem originally from the Latin soldier exercise term. Or to be more exact it seems to have morphed from the Latin 'exercise of soldiers in fighting' to 'army, body of soldiers' then finally to scrap.
After a quick recce around it appears that the Roman word for a battle in the modern sense was in fact pugna - 'conflict' . (But I could be way wrong with that!
. Looking up the English-Latin translation for battle, no modern Latin term seems to have the battuere verb root)
(Below from the Online Etymology Dictionary:
http://www.etymonline.com/index.php?term=battle)
battle (n.)
c. 1300, from Old French bataille "battle, single combat," also "inner turmoil, harsh circumstances; army, body of soldiers," from Late Latin battualia "exercise of soldiers and gladiators in fighting and fencing," from Latin battuere "to beat, to strike" (see
batter (v.)). Phrase battle royal "fight involving several combatants" is from 1670s.
battle (v.)
early 14c., "to fight," from French batailler (12c.), from bataille (see
battle (n.)). Related: Battled; battling.