I would say its quite difficult as the names are used both to define a group of chilies and certain cultivars.
As a pod shape / group of chilies both falls in to the category of Wax Types / Yellow Wax - including both a shorter "fatty" version fairly thick fleshed creamy yellow /light green chilies that matures to orange/red and the elongated chilies around 10-14 cm. Both pendant and upright fruits are found..
The elongated variants are called Hungarian Wax or Banana Peppers, which many use as synonyms.
Hungarian Wax, Banana Peppers are likely to have been released US around 1940 and as far as I remember from reading having been brought to the U.S. from Hungary aorund 10 years before by Corneli Seed Company (Jean Andrews).
The Banana Peppers with no heat in the US are probably also from Corneli Seed Co
"Sweet Banana - Breeder and vendor: Corneli Seed Co. Parentage: From a mutation. Characteristics: Thick, sweet flesh wall, bright yellow color, proper shape and size for pickling. Similar: Yellow wax types. Adaptation: wide" (Corneli Seed Catalog)
Defining certain cultivars / variants within the elongated Hot Wax and Banana Peppers is difficult as the names are used both as a group of peppers with fairly similar features and as cultivar names - Hot wax, Hungarian Banana Peppers, Hungarian Hot Wax, Hungarian Sweet Wax, Hungarian Yellow Wax, Hungarian Hot Wax, Hot Bananas, Sweet Bananas.
To make the matter more confusing there are large amount of other names labelled as Banana Peppers: For instance the F1s Biscayne Hyb, Inferno Hybrid, Sweet Savannah, Budapest hot Banana, Surefire. I can imagine that it is not only in Nother Europe that the Nurseries and markeds do not use the proper F1 cultivar name from the vendor, but just list the plants as Banana Peppers.
Some btw. use Hungarian Wax as and indication that is it a hot pepper, while Banana Peppers are used to indicate that they have no heat. Others don't make a distinction.
As an heirloom cultivar it seems to me that the Hungarian Hot Wax are yellowish and broader, than the Hungarian Hot Waxs that are sold by many seed vendors - at least in Europe, which are light green, ship the yellow phase and go directly to red, also with thinner flesh. And the majority use the term Banana Peppers for the broader versions, and sometimes the more creamy yellowish - but often its just a big blur
My hungarian waxed would turn as orangish-red or even redder than what Prehensile has pictured BUT when they get to be around that shade I had to keep an eye out for BB-sized rot spots starting. I seldom left them on the plant that long though, usually by that point the plant was begging for some weight reduction so the branches didn't bow and snap.
Yes, carpboy, they sure do. Definitely worth trying, they're one of the better C.Annuums when they're ripe. May I also suggest ripe red Serranos, Poblanos, and Jalapenos. Man, they get so sweet and have an apple-ish taste, especially the red poblanos. Mmmm.
Not growing any this year but in past years my Hungarian Waxed were a bit wider and pointier than what Prehensile pictured, more like the following (not my picture) but I usually waited until they at least had an orange blush to pick 'em:
The first several would grow upside down but after that gravity had its way on the rest.