The question has been answered well enough... But, despite everyone saying AES is wrong, there are bits of evidence that AES can be used as a subtitle to set it apart from the MVS. Home system main boards and parts often have AES, AEP or AEC written on them. Various booklets have AES in them as well. The logo has "Advanced Entertainment System" stuck inbetween Neo and Geo. It's possible that AES was only used on English home system packaging.
Going by other SNK documentation (like the programming guide), I think they internally called the two platforms MVS and Neo Geo. That doesn't help much since MVS is still a Neo Geo and the home system needs a subtitle too... Otherwise they're both Neo Geos.
So, for better or worse, AES and MVS are here to stay. I don't mind using AES by itself, but seeing "Neo Geo AES" makes me cringe. It looks horribly tacky. The home system in a perfect world should JUST be Neo Geo, nothing more. Neo Geo MVS isn't as bad, but MVS works fine too.