This is one of the debates and things that drive me crazy as I have posted elsewhere on our Purslane-Portulaca forum her on ATP.
They are "kissing cousins" but not the same plant although most growers make the labels the same. Here is my guide for you:
Purslane = plumper oval leaves
Portulaca = spiny leaves.
Also, generally purslane has 5 single petals. There is a double I have seen but never in person.
Portulaca is ruffled blooms with layers.
I'd also love you to take a little bit of time to browse through the forum and look at some of the beautiful photos people have posted. It will help you identify the two.