Moved from Narrow-winged Damselflies.

1) Damsel landed horizontally on surface
2) She holdes her wings above the abdomen
3) Dark stripe on side of thorax "Y" shaped or pinched shut.
Yours is three for three. We say genus Argia.
It's a female, and we would say blue form female of the Blue Fronted Dancer, Argia apicalis.
Another book we would recommend for you (if we haven't already) is Damselflies of the North Woods by Bob DuBois, part of the North Woods Naturalist Series. It has wonderful photos by Wisconsonian Mike Reese (who also has great damsel images on his Wisconsin Butterfly website.)

...these are two different damselflies, I believe, rather than male and female of the same species.

Odonata Central (http://odonatacentral.bfl.utexas.edu) has checklists by state and by county; I looked up your county and that cuts down the possibilities considerably (though you might have a stray from a neighboring county, of course.) Though at the moment I don't have time to search BugGuide's pages for those species, I suspect that some image here will fit, when you, or I, or someone, has time to chase down the Grant County, WI species. I'm guessing one of them is a dancer (Argia sp. and the other might be, or might be a bluet (Enallagma sp.) You're way out of my geographical range, though, so I can't use my favorite "south central" guide.

Elizabeth