This summary is not the rule. The rule text controls.
When someone wants a court in Oklahoma to recognize a judgment from another country, there are two ways to bring up the issue, depending on the situation.
If there's no existing lawsuit already happening, the person seeking recognition has to start a new court case just for that purpose. This means filing a lawsuit specifically asking the court to recognize the foreign judgment as valid.
If there's already a lawsuit going on between the parties, the person doesn't need to start a whole new case. Instead, they can raise the issue of recognizing the foreign judgment within that existing lawsuit. They can do this in a few ways: by filing a counterclaim (a claim against the person who sued them), a cross-claim (a claim against another party in the same case), or as an affirmative defense (a reason why they shouldn't be held liable, based on the foreign judgment).
This rule basically gives people flexibility. It lets them handle the recognition issue in whatever way makes sense given their circumstances, rather than forcing everyone to file separate lawsuits even when they're already in court for a related matter.