Right board, I think. And very definitely a good question!
My short answer is: if the spray is cheaper anyway, then I'd go for that one. You might get a stronger concentration for less money. Yay! More stink for less bucks has to be a good thing!
My long answer: (you can start yawning now if you like...)
Eau de Cologne can be one of two things:
There's the 'classic Eau De Cologne' which is a particular recipe that is fresh/citrus and I won't go into it here. The boys can tell you about that if you want chapter and verse (there was quite a bit of discussion about it recently on the emergency board. I learned a lot from the boys. Very precise, some of those BN boys).
Or there's 'eau de cologne strength' of many perfumes available (I've seen lots of Guerlains) and if I remember correctly, that means there is 5% jus in the mix. It's the lightest concentration available and great for splashing on merrily in the summer without asphixiating your colleagues.
I think it's possible the SA is telling the truth. The greatest likelihood is that it's an older company that uses old-fashioned terminology. Just as I often use the British term 'scent' as another word for 'fragrance' or 'perfume', I'm sure I've read in US books people using the word 'cologne' as just another word for 'perfume' or 'scent' or 'toilet water'.
Things haven't always been as uniform as they are today. I have an oldish bottle of Jicky eau de parfum and it's called a parfum de toilette. It's definitely way stronger than the edt, so I assume this is their old name for the edp strength.
Does this help?