There are several differences. Keeping in mind that the BA is a first degree and thus includes basic studies in chemistry, physics, statisitics and mathematics as well as in the humanities, the degree might be thought of as both broad, technical and professional but with the limits that training in the field is limited and that it is in a sense at least more theoretical than practical. The second degree, the MA assumes that the individual already has the basics of a broad education and can thus focus more intently on turning the theory into pragmatics both in the classroom, the laboratory and in the field. In almost all cases (and certainly at the better universities in the USA and Europe), the MA also has a requirement for a thesis and that involves an in-depth study of one specific field within the academic field. Not all who do the MA do a first degree in oenology/viticulture and thus have the requirement to do some "make-up" courses to bring them to the desired level.
Anticipating a first question - I do not believe that a second degree is always necessary in the wine field, that depend largely on how much one "gets"/"takes" from the first degree and the experiences one gathers when starting in the field. Working under a truly excellent winemaker can be the most valuable of experiences. Many who have a BA in some other field will thus do a second BA, this one in oenology rather than going on to the MA and then out to the field, and that can make good sense.
Anticipating a second question - as to whether formal university studies are necessary for the future winemaker/oenologist..... The contra-example has always been the many French and Italian families, some of whom produce some of the best wines of the world and who have never attended college or university. Quickly, quickly, however, those days are on the way to being forgotten, the best-established families of Burgundy, Alto Adige, Priorat and even Greece and Turkey are sending at least one child to university in order to gain the technical knowledge that is so necessary.
And now, anticipating yet a third question: Is it necessary for all winemakers to attain a BA or an MA in oenology? I'd say in a best of all possible worlds, yes, but the world is far from perfect and it continues to be possible for a winemaker, especially in an artisanal or boutique winery to manage without such a degree, picking up the knowledge so to speak "as they go". Such winemakers do, however, need fallback on colleagues who can help them when it comes to problems that they encounter and, truth be told, some will succeed marvelously while others will not. As to the winemakers at anything more than a boutique winery, I cannot help but believe today that such a degree is absolutely necessary.