Русско-англо-русский юридический словарь

In civil procedure, a party's claim is a counterclaim if the defending party has previously (in the present action) made a claim against the claiming party. (Wikipedia)

A defendant who has a claim against the plaintiff can bring what is known as a counterclaim, and at that point the defendant becomes what is known as the "counter-plaintiff" with respect to the counterclaim against the plaintiff (who is now also known as the "counter-defendant"). (Lawyers.com)

A crossclaim is a claim asserted between codefendants or coplaintiffs in a case and that relates to the subject of the original claim or counterclaim according to Black's Law Dictionary. A cross claim is filed against someone who is a co-defendant or co-plaintiff to the party who originates the crossclaim. In common law, a crossclaim is a demand made in a pleading that is filed against a party which is on the "same side" of the lawsuit. (Wikipedia)

A defendant who has a claim against the plaintiff can bring what is known as a counterclaim, and at that point the defendant becomes what is known as the "counter-plaintiff" with respect to the counterclaim against the plaintiff (who is now also known as the "counter-defendant"). (Lawyers.com)