Horiz/Vert Biamping

I see many references to horizontal vs vertical biamping and the definitions seem to be contrary to how I would define these: I would define them as such:

Vertical: Defined as one amp for the Top freqs and another amp for the Bottom freqs.
Horizontal: Defined as one amp for the Left channel and another for the Right channel.

But these above definitions do not seem to be what anyone else here uses so I am curious as to why they are defined exactly the opposite.

And I can see there would be one major advantage for each situation. When the amps are matched, better channel separation would be expected if an amp is used for each channel. But to have an amp for the top and one for the bottom might bring on more openness in the mids and highs as the amp driving that range is not stressed by the low freq demands on the same power supplies in a stereo amp. I guess true dual-mono stereo amps would alleviate this or is this still not entirely the case? Or is it really a better way to go with a different amp optimal for each of the 2 freq ranges? And if so, what about synergy around the crossover point between the two amps' sonic differences?

Any thoughts or experiences here would be greatly appreciated. This mainly pertains to Magnepan Series 3s but other speaker usage would be interesting.

Thanks.....John