There must be male and female trees, because we have had some that flower, but do not set seed. Maybe someone else can answer that for you. I do know that the bees really work the one that does set seed for us.

There is one point of confusion that really "threw me" for the longest time. While travelling in Europe (Russia), I had the occassion to be offered a light yellowish creamed honey with an unusual (but tasty) flavor. I was told it was honey from the lime tree. Well, I knew lime, right? The green citrus fruit that required a climate much more tropical than this close to the artic circle! My mind was suffering a real "disconnect" here...how is this honey from a lime tree? Must simply be a translation problem...

But this is typical of the problems you run into when the common names of plants are used. A little internet searching upon my return home and before you know it, the discovery was made: Lime tree = Linden tree = Basswood tree.
And the Winter Linden tree (Tilia platyphyllos) is what had provided that wonderful tasting Lime honey! And this honey tasted different from the liquid (extracted) honey from the American Basswood (Tilia americana) so common in your part of the country.