I'd differentiate between a singular contra dance - longways sets, duple minor (some triple minor chestnuts in special cases e.g. The Young Widow), jigs/reels typically (except exceptions as discussed). I would characterise them choreographically as ideally linked figure to figure in a continuous progression. I think (even though the etymology is spurious) I would want to have the feeling of a contrary person as well as my partner.
A contra dance evening might well feature the other styles particularly if it's a one-off party etc. but I would not say they are contra dances themselves. Similarly square dances are not contra but might make an appearance in this context.
I'd be more inclined to include the non-contras in an "American" night at a festival rather than at a "contra" night.
Ted Sanella and Larry Jennings quite clearly included these styles in their books but in seperate sections to the contras.
So yes, I think I agree with you Colin.