Linguistics term for blurring words/sounds together

When you sing the alphabet song, there comes a point when you hit “h, i, j, k, elemenohpee”. I wouldn’t quite call it a contraction since there aren’t any sounds being dropped. I’m struggling to come up with a better English example off the top of my head.

Anyway, does that fall under the umbrella of elision or is it something else?

In addition to the terms contraction and elision that you’ve mentioned, there’s syncope:

But I’m not sure any of these terms would apply to the specific example you gave, that just seems like a speed difference.

Synaloepha?

As you said, there’s no sound being dropped; no sound being elided. The fact that the syllables flow together nicely doesn’t change that.

The “liaison” phenomenon in French comes to mind (words that, in their own, would be pronounced separately and/or with silent letters at the end are pronounced in full and flowing into each other when in a sentence).