Normally, a wine fridge (Perlick uses the term wine reserve) is used for wine storage. Some have one temperature and others have layered temperatures for different types of wines. A beverage fridge is basically a refrigerator designed to chill beverages to relatively cold temperatures (colder than tannic red wines want for aging, anyway).

There is at least one recent thread addressing this subject in more detail that you may wish to search out.

"Undercabinet" _may_ refer to the finish on the top and sides, that is, you only get pretty stainless steel on the front. This may vary with manufacturer.

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Built in fridges rest on the floor in between two cabinets. This means that to build it into the oven cabinet the opening has to be pretty exactly 24", and the oven platform may need to be stained or otherwise finished out in order to look right in the recessed toe area that will now be sitting on the platform. You may have room left over vertically, which you could also finish out and install wine glass racks onto the underside of a newly installed drawer box to have a pull out wine glass rack below with corkscrews and other paraphernalia in the shallow drawer above.