Portulacaceae includes plants called Purslane and Portulaca. Most of these in the above photos are actually called P. umbraticola and the paddle like leaves are what defines it and compares it to P. grandiflora. All over the country and perhaps the world there is mass confusion about the latin names and I have found even some nurseries are confused. I was given a lesson by a grower and this is my take on the purlane plants which I adore.
P. Oleracea = Wild plant with small yellow (usually) flowers and it is edible.
Portulaca: P. grandiflora = Showy, many colors, spikey leaves, double blooms. Called Portulaca by most nurseries and growers. Some call it Moss Rose.
P. umbraticola = Showy, many colors, usually a single petal formation but there are more doubles showing up. The leaves are paddle shaped. Called purslane by most nurseries and growers.
(This is what I posted in comments and I requested them to be moved to Purslane- wingpod plants.)