You said...

"...but lets assume DM demanded $2 mln as a settlement based on XYZ, and the defendant says no, your XYZ claim is in error, we only did this or that, and we will offer you 1/2. That's a counter claim right?"....

No Joe, that is not it a counter claim...

A counter claim is :...

A counterclaim is made by the defendant to a civil proceeding, in a main action against the plaintiff or against the plaintiff and other people. This claim may be an attempt to offset or reduce the amount/implications of the plaintiff's original claim against the defendant, or it may be a different claim. Counterclaims did not exist at common law; they are an invention of modern civil procedure. (Look the full text at Wikipedia)...

For example Imation asserting that EDIG is infringing on some of their patents and they want redress against EDIG...

Gil...