imo there is a difference:
mercs are usually a private enterprise soldier who is well versed in all combat situations (almost always armed to the teeth) and is usually hired to protect (political reasons) or assault. killing is optional.
assassins are professional murderers usually hired to get rid of someone(s) with the assumption of complete success and without the murder(s) being tied to the person who hired the assassin. killing is virtually their only goal.
deadshot, bullseye, etc = assassin
punisher, 90's cable, etc = mercinaries