Simply seeing the opponent's movements is not enough. You must learn to hear, feel and smell the opponent's intentions. Perception speed is defined as the time it takes you to mentally register the opponent's intentions once you first sense his offensive or defensive stimulus. You must learn not to concentrate too much on details. Look at nothing, but sense everything.
Awareness is never exclusive, it includes everything.
A mind must be wide open to function freely in thought. Once you have sensed the opponent's intention, you must decide how to respond. Your decision speed is determined by the length of time it takes you to sense the opponent's stimulus and select an appropriate response. Your ultimate goal is to be able to respond quickly and instinctively. The time that it takes to transfer your decision to punch from the brain to your fist, and actually begin the punch, is your initiation speed.