Conn only used the terms Baritone or Euphonium to distinguish, and those terms were only really meaningful in the Artist era. I use the term Baritone Saxhorn to specifically indicate an instrument having some cylindrical tubing (~25%), as opposed to the minimum, and a size profile which is visibly above the average (Tenor Saxhorn / British Baritone). Being any more specific than that is basically impossible.
Your Holton does appear to have the proper bore profile of an American Euphonium.
Again, this distinction is most important in mouthpiece requirements. I was really disappointed in the performance of 1924 model 64-I. The Precision era version is probably leaps and bounds superior. For an idea of mouthpiece size difference, a JK P12F is barely small enough for the Besson 2-20 front action Baritone. That's 24mm cup diameter, cup depth around 6.75C, and 5.8mm throat. I could maybe improve performance with a larger throat, but I'm not willing to invest further in it. I already had to custom order that mouthpiece. I don't know what the stock mouthpiece would have been, but it wasn't the Besson 10.