“compulsory counterclaim”和“premissive counterclaim”分别指两种类型的counterclaim。

“counterclaim”指反诉、反请求。指在已经开始的诉讼中的被告通过法院向本案原告提出的一项独立的请求，以代替就该请求对原告另外提起一项单独的诉讼。

在英国，被告要提出反诉时，可在其答辩状中对作为其反诉请求根据的事实另加陈述，并提出其请求法院给予的救济。被告反诉的被告不限于原告，还可以包括应与原告一起就本诉标的向其承担责任的其他人。另外，原告对被告的反诉在一定条件下还可以再提出反诉。法院可以对本诉和反诉一并作出判决，但如果对反诉难以和本诉一并作出处理时，法院可予驳回，这种情况下，被告必须另外提起交叉诉讼〔cross action〕。

compulsory counterclaim强制性反诉，即当被告对原告的请求与原告在本诉中的请求有逻辑关系，且是基于同一事项而产生的时，被告必须在原告提起的诉讼中提出反诉，否则，在本诉判决生效后，被告将丧失另行起诉的权利，但有例外；A compulsory counterclaim is a claim made by a defendant against a plaintiff that arises from the same transaction or occurrence as the plaintiff's claim. The claim is compulsory in this situation in that it must be raised in the defendant's answer, or it is waived.

permissive counterclaim选择性反诉，即如果被告对原告的请求与原告在本诉中的请求不是基于同一事项而产生的时，被告可以自行选择是否提出反诉。

A permissive counterclaim is a claim brought by a defendant against a plaintiff in the situation where the defendant's claim does not arise from the same transaction or occurrence as the plaintiff's claim.

以下为相关双语示例，供参考：

Permissive Counterclaim. A pleading may state as a counterclaim against an opposing party any claim that is not compulsory.

选择性反诉。诉状可以将任何非强制性的请求称为针对另一方的反诉。

Compulsory counterclaim. A pleading shall state as a counterclaim any claim which at the time of serving the pleading the pleader has against any opposing party, if it arises out of the transaction or occurrence that is the subject matter of the opposing party's claim. 

强制性反诉。诉状应将任何于送达诉状时答辩人针对另一方提出的任何请求称为反诉，前提是该请求源于作为另一方请求标的的交易或事件。