I set up the corner blocks to look at so I could figure out which one I wanted, but the double 3-way corner and the double prism corner don't seem to have any differences.

I've arranged them with the same alignment, put up signs, and labeled the sides. The screenshots below show all 6 sides.

And here's the F3 screen confirming I haven't done a stupid and just placed the same one six times (which I initially thought I'd done and I've checked a bazillion times because they are so similar)

Here's a better shot of the tops

That is intended. The double prism and double threeway corners are only noticeably different when at least one of the two parts has a transparent or semi-transparent block applied to it.