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Some of the attributes you ascribe to European "tenor tubas" are also true of older Martin euphoniums. The old Martins were wrapped taller/wider than compensating euphoniums, had fatter bottom bows and outer branches, and narrower leadpipes. Martin would make these in any configuration you wanted--top action pistons (3v, 3+1 and 4 inline), front action pistons, and even with rotary valves (there aren't many of these out there, but they do exist).

I've attached a picture of a Martin next to a Besson, for reference. The Besson has an 11" bell and the Martin's is 11.5".

Two other cool features of these old Martin euphoniums:
-The upper register plays very well in-tune, with none of the extremely sharp notes that plague compensating euphoniums.
-Like older American tubas (and unlike any compensating euphonium I've played) they have usable "false tones." The three valve Martin pictured below can be played chromatically down to the pedal, using a false tone series starting on "low Eb."

-Funkhoss

In my book the difference is all about color or loudness.
HAHAHAA all euphoniums fit in one case size!
If not fitting in that case, must be another name.

I think it is a distinction without a difference.

There is still one big difference between the German Baritone (oval) and the German Tenor Tuba (straight): the oval horns were developed in the late 19th century and most of them are still the same, only valves are better machined and valve operation is upgraded. So I am amused when non-germans are a bit surprised when trying those brand-new antiquities and find no way to love it. Some years ago I had a student playing a four valve oval baritone from one of the big german brands, made in the 1980s and owned by our village band. When her parents deciced to buy her a horn of her own I found a very nice Besson (London) Class A "Prototype" 3+1 Saxhorn (Euphonium, Baritone, however you call it). After two weeks playing the Besson she tried once again the oval one and said: "how can one play this crap..." Then I told her the age of her new horn, it was made in 1919... Btw, she was 14 and playing for two years!
The real German Tenor Tubas were, like their bass and contrabass cousins, improved over the years, so they are much better in intonation and sound. But here in Germany they are quite rare and a lot of people don't even know about their existence and being another species. The improvements on the oval horns started in the 1990s, but for this instruments you pay a lot of money and the improvements are only to find on very few models. Most oval horns are still as modern as the Wessex Ophicleide...

I like homogenized.

I tried Uber healthy whole raw milk once and said “how can one drink this crap..."