Is there a grammatical term to distinguish the different functions of the verb "married"?

Sense 1:

The husband married the wife.

Sense 2:

The priest married the couple.

Is there a grammatical term that characterizes the different ways the verb is used in these two senses? I'm struggling to articulate exactly what the pattern is, but it has something to do with the manner of participation between the subject and object. In the first sense, the subject is changed as a result of the verb; in the second sense, the subject causes the objects to change (without changing themselves).

Another seemingly similar example (even though it may be an incorrect usage) is:

The participants consented to the research.

The participants were changed through the process of consenting.

The researcher consented the participants.

The researcher completed a formal process of obtaining consent, but wasn't involved in the consenting; that is, the researcher caused the participants to give consent.

As Dave mentioned in one of the answers here, this phenomenon is based on the transitive property of the verb.

The term you’re looking for with words such as marry is Patientive Ambitransitive Verb.