Can I download the Yosemite install "app" on a MacBook Air, move it to an install USB drive, and install it on a MacBook Pro? That is, is there a difference between the Yosemite install "app" that I would get on the Mac App Store, between the one I would get on a MacBook Air vs. on a MacBook Pro?

Trying to download it on my Air and install it clean on my Pro.
The Install App that you download from the Mac App Store is a universal installer that isn't tied to a specific model/build.  Similar to the retail installation discs from earlier operating system releases.  It will install properly on any supported systems that meet the requirements.

So yes, as long as the installer is from the Mac App Store then you should be able to copy it to a thumb drive and install it on any supported Macs.