I've tried both Magnesium Glyconate and Magnesium L-Threonate and both have helped my sleep, Magnesium Citrate did very little. Which makes sense, the latter is known to not be absorbed very well.
I've not noticed any significant difference between the other two.
Magnesium citrate works well for constipation, IME.
Yeah, magnesium citrate is used medically as a laxative. Because it is poorly absorbed, it draws water into the stool osmotically, making it softer. (But that also draws water out of the body and can be dehydrating.)