I think Verdolaga is just another common term for purslane, so that probably doesn't tell you much then.
I'm most familiar with P. oleracea, which is supposed to be the best species for eating. P. umbraticola...have you ever seen 'Yubi'? I saw something about it...it is designated a Texas Superstar plant, so I might try that sometime if I can ever find it! Still edible, unlike the Moss Rose at HD.