The only difference between an action at law and a counterclaim in a court of record is that the original parties have their identifications changed. The defendant becomes the counterplaintiff, and the plaintiff becomes the counterdefendant. Other than that, the counterclaim is written the same as an action at law.
A court of record proceeds according to the common law. It is not a criminal court and it is not a civil court; those two courts are statutory courts, not common law courts.
Also, note that in every county there is only ONE court. The court is typically subdivided into divisions. No matter what division you file the case in, it is still the same court. When you file a common law case the clerks typically don't know what that is and tend to classify it as a civil case. Sometimes in the Federal courts it is filed as a "constitutional court" case or a "miscellaneous" case (which has a lower filing fee).
It is not necessary to argue too much with the clerk. If the clerk is too ignorant to do it the right way, don't worry. If the clerk doesn't like the caption at the top of the page, don't ask what you should do because he cannot give you legal advice. Instead, you ask him what he requires: he can tell you that.
Changes to the paper can be made on the spot by hand printing IF you print very clearly. Hand printing is legally the same as typewriting. If the clerk objects to the term "counterclaim" you may change it to say "complaint". It doesn't really matter because it is the actual text in the body of the paper that is the substance. Titles, headings, and other items in the caption are merely aids to understanding. The substance of the paper is what controls, not the titles and headings.
There are two kinds of trial courts: superior and inferior.
The criminal court is an inferior court because it is operating according to special rules (criminal code) and not according to the common law. Even if its name is "Superior Court of ....." it is still an inferior court so long as it is operating according to some code or statutes rather than the common law.
On the other hand, a court of record, so long as it meets the criteria, is a true superior court.
The decisions and proceedings of an inferior court are not presumed to be valid. The inferior court can be sued in a superior court (that's called a "collateral attack"). In other words, the superior court (court of record) out ranks the inferior court not of record".
When you do a counterclaim, the primary issue is jurisdiction. By what authority does the inferior court presume to take jurisdiction over the parties? When the counterclaim is filed, all parties in the inferior court, and the inferior court itself, are served with the suit. Because the primary issue is jurisdiction, the proceedings in the inferior court must stop immediately and may not proceed until it proves in the superior court that it has jurisdiction. If it fails to prove its jurisdiction, then the final judgment of the superior court will be that the inferior court had no jurisdiction and all proceedings thereafter are barred.
If the inferior court proceeds anyway, then contempt proceedings and judgment enforcement proceedings can be initiated in the superior court.