My personal understanding:
Anti-Terrorism = the practice of using intelligence, political, social, psychological, criminal, analysis to predict where an attack is likely to happen and then using that anticipation to apply measure to harden against the possibility of the terrorism attack. Basically an effort to reduce the likelihood of the attack by making a target to difficult to attack.
Counter-Terrorism = the same practices of “Anti-Terrorism” but instead of hardening in anticipation of the attack, the possible terrorist (or actors) are targeted for capture to gain further intelligence and to remove them from the equation. Or it can be the targeting for killing the terrorist (or actors) to eliminate the threat they posed. Basically an effort to stop an attack by going after the attackers or removing their ability to attack.
This is my personal understanding of the two, I am not staying they are correct or that there is not more that goes into the two of them. My question is how would you personally define the two based on your understanding?