Curiouser and Curiouser

When I was in my last year of undergrad at UCLA, I took Linguistics 10, which looked at the etymology of words. I mention this because earlier today I asked about the word for “three times a year”. The answer was triannual, whereas triennial was every three years. So (I wonder): was there an etymological difference?

Triannual: tri ‘three’ + annual (from the Websters New Millenium dictionary); origin: 1630–40; tri- + annual (per Random House)

Triennial: 1640, “lasting three years;” 1642 in the sense of “occurring every three years,” from L. triennium “three-year period,” from tri- “three” + annus “year”

So, they both seem to be “tri” + “annual” (or annus). So where and how did “-annual” get the sense of part of a year, whereas “-ennial” get multiple years? Further, if that is indeed the case, wouldn’t semiannual therefore be equal to biennial, given that 1/½ = 2? Should it be semiennial?

I’m confused.

[My wife’s response: She knows, but good doctors are expensive.]