Quick Strike was replaced/renamed Alpha Strike. Like BattleDroids became BattleTech. It's not a separate game (from Alpha Strike).
Both AS and BF use the same condensed stats. BattleForce is intended as a scaled up BattleTech, where you control a lance as a playing piece rather than a 'mech/vehicle/etc. Alpha Strike is a hybrid between the two. It uses the condensed stats of BF, but keeps the focus on single 'mech/vehicle as a playing piece.
Alpha Strike is based on a single unit moving/attacking, and it's scaling is (mostly) the same as BattleTech (just converted from hexes to inches). So the movement to range ratio is almost the same as BattleTech. An Alpha Strike unit can attack at long range up to 48" (24 hexes). Ie. It's roughly the same scale for a single unit as the playing piece, same ranges, movement speed, etc. (Roughly).
BattleForce changes the scale, one BF turn is three BT turns, one BF hex across is three BT hexes across, so that ranges are divided by 3 (long range is 8 hexes, not ~24 hexes of BT). Instead of moving a single unit, you move a lance/star/level II as a single playing piece.
That range difference and moving one 'mech/vehicle or a lance as a single piece are the major differences. There are other differences that come from those two (like AS having different movement modes, BattleForce having a command system, etc).
