I studied magnesium like a full-time job for a month or two so I can help you out with that. Magnesium chloride was the best supplement I came across whenever I went through forums and the websites of experts. By applying the magnesium chloride, or magnesium oil as it is also called, to the skin, your body will absorb more of it as it dissociates completely at skin pH. As long as you leave it on for 20 minutes you get a lot of it in.
Elemental just refers to the magnesium itself, someone getting a form of magnesium in a 1,000 milligram tablet for example, may only be ingesting around 100 milligrams of elemental magnesium, with the molecule or compound it is chemically bonded to accounting for the other 900 milligrams.
Chelated forms (ending in -ate) such as citrate, taurate, glycinate, threonate, the list goes on, are the best forms of oral magnesium. Citrate seems to be the one (out of the chelates) that causes the greatest increase in bowel movements, as magnesium travelling through the digestive tract causes water to be brought into the gut leading to diarrhoea. Glycine combines magnesium with the amino acid glycine and is a double whammy for anxiety as glycine is an inhibitory / calming neurotransmitter that people use as a sleep aid. Taurate is another good one but I avoid all oral forms of magnesium to prevent any bowel irregularities and get maximum absorption. Even if you have food poisoning and bowel inflammation / permeability, that will not be a problem with transdermal magnesium.
However, even with the effect of ingested magnesium increasing water in the gut and relieving constipation that way, there are still constipation-relieving benefits from having magnesium transdermally as simply increasing the body's magnesium levels are enough to aid constipation by reducing muscular spasms of smooth muscle which typically cause constipation.