ARGH!
Tuning can't be a factor because the GCEA is only one of several "standard" tunings for a uke, all of which have been used in the past or are still used today. Regardless of the pitch, all ukes are tuned in the same relationship between strings. Baritones can be tuned low or high-D, or even GCEA. It is that relationship and the number of strinsg that determine if it is a uke.
Size can't be a factor either because the soprano wasn't really standardized until into the early 20th century -both concert and tenor are additions after that. And there are some manufacturers today who vary from the "standard" scale lengths.
Baritones are EXACTLY ukuleles. Enough with this anti-baritone-ism!