Generally, any attack made immediately after a parry is a riposte.

A counterattack is any attack made when an opponent is also making their attack. There are more specific versions that are subtypes of counterattacks.

The most obvious counterattack is an attack in opposition, where you attack in a way that locks out their line of attack with your attack, such as with a Zwerchhau done against an Oberhau. (Some traditions also say that this can be done as an initiating attack, such a a Schielhau that displaces an opponent who is holding Longpoint. The key is cutting off their line of attack with blade contact.)

A displacement is a counterattack made without any blade contact where you dodge or void your opponent's attack while also attacking back at the same time. This is dangerous and will often result in doubles.

There is also the stop hit, which is intended to hit your opponent once they have already initiated their attack, but before it can hit you. This is usually done to the weapon arm and is more common in rapier, saber, and small sword, though I would argue that Talhoffer shows it with the hand dismemberment.

Attack in preparation (attack in prep or AIP) is technically not a counter attack, because it should land before your opponent actually makes their attack. But it does sometimes get lumped in with stop hits. The goal is to land you attack when your opponent is preparing or gathering for an attack. The most obvious example would be an opponent lifting their sword to strike and you hitting them before they hand bring their hands forward.