My recollection is that biggest difference is which stats they work off of. For a counter, you need a high agility to dodge the attack, and then a high technique to trigger the counter it. To make a thrust back, you need a high defense to initiate the parry, and then high technique to trigger thrust back. High defense is also needed to trigger a weapon or shield defense, but that just blocks the attack.
It definitely is a complicated system, that unfortunately has very little impact in gameplay. Many of the characters that can effectively make some kind of counter attack, have equally high defense and agility, so it's something of a moot point whether they rely on one or the other. And of course, at the end of the day, in particular due to the limited skill slots and rune slots, it is not really viable to run a "counterattack character*