I think this is one and the same thing. I didn't actually have a CNI to start off with, I had a License to Marry from the Isle of Man. Different name, same thing. Then I exchanged it for a CNI at the Manila UK embassy.

I have an idea that a Legal Capacity to Marry is actually an Amercian expression....

When I was starting off last year I was worried about the Isle of Man License to Marry, so I emailed the UKBA in Manila and they confirmed it was okay.

I am not absolutely certain about this but someone else might confirm it one way or another.

In Australia the 2 expressions are interchangeable....