The term 'English Country Dance' refers to the particular form of a dance, in the same sense as Polka or Waltz. Usually by the end of the 18thC it was longways. You once did this at a Ball, Hop, Dance or in the kitchen or the mud. In France you may have done it at a Bal.

You didn't do it at an 'English Country Dance' any more than you did a Polka at a polka or a Foursome reel at a foursome reel.

But a 'dance' could refer to the actual event, and everyone would know what they were going to. If you go to a dance now it could be anything, hence the very recent requirement for a further definition.
So it has become customary in England to use the (not stolen, as they haven't been alienated) terms ceilidh/eceilidh to mean a dance where you may expect not just lively ECDs, but Polkas, Waltzes, etc, and have some good fun.

This will be understood to be a different sort of event from a Country Dance or a Dance 4Dancers.

Wherein lies your point/problem?