As an English person who moved to the USA as an adult. I thought I might give my side of what I have seen here to explain the difference in wording. Firstly I would highly recommend reading the Wikipedia article on this as it includes a discussion of why "pound cakes" and other similar cakes are considered sponge cake in the UK but "foam cakes" are in fact not, while the situation is largely reversed in the USA.
In my experience in the UK, cakes encompass a similar but significantly different set of foods then they do in the USA. These include far denser baked goods than would normally be considered cakey in the USA. This includes rich fruit cake, eccles cake, welsh cake and various other heavy, rich or chewy baked goods. In general it feels to me that cake is more about the role the cake fills in a meal than it's specific texture. Sponge cakes are light and spongey compared to most of the other things called cakes so the term is still appropriate, and helps distinguish these lighter cakes from other cakes.
Since coming to the US I have noticed that the range of goods people assume to be cake tends to be much more on the lighter fluffy side, including angel food cake, chiffon cake, but also includes things like funnel cake, which does not seem intuitively cakey to my British palette. It feels like cake in the USA depends much more on the texture, with most cakes being much lighter, fluffier affairs, with denser or more chewy cakes being the exception that requires specific calling out.
So, down to the actual question. The British definition of sponge cake, I think comes down to the typical style of the lighter end of cakes in the UK, which are mostly pound cake like, cakes which one would often eat with tea or coffee, including Victoria sponge, Batternberg cake, etc. The style of very light fluffy cakes common in the USA seems to be a much more modern trend in the UK so are not what one would jump to when thinking of sponge.
Conversely sponge cake in the USA occupies a different space, though shares the fact it describes cakes on the lighter, fluffier end of the spectrum of typical cakes in the USA. Comparatively pound cake and other batter cakes are actually fairly heavy on the spectrum of common cakes in the USA (excluding celebration, wedding and birthday cakes). I also noted that batter style cakes seem somewhat less common in general in the US, and are often seen as antiquated or old fashioned.
In summary, I believe the term "Sponge Cake" has entirely different origins in the UK and USA, with the definition being just similar enough to be confusing. The spectrum of cakes available is generally very different between the two countries as well as what is a cake at all.
Basically, to make things simple, consider "American Sponge Cake" and "British Sponge Cake" to have different meanings, and avoid conflating the two, as trying to combine the two definitions results in a helplessly vague term with little agreement on what it means.
Very many terms in British and American cooking vary, dumplings, biscuits and many other things with the same name are totally different foods, roasting, baking, grilling and broiling seem to have significantly different meanings. In essence try not to assume a food, cooking method or other cooking related term means the same thing in a UK or USA context. This is very often mistaken and in fact the similarity of language and words is often a false friend, misleading one to assume the same words likely have the same meaning where they do not.