Are they the same? White and pink http://en.wikipedia.org/wiki/Calyptridium_umbellatum it is now Cistanthe umbellata, Family: Portulacaceae I clicked at Genus: Cistanthe and I have different Family: Montiaceae Which family would be correct for my plant?
Montiaceae is what is currently used. And, you'll find as many references using Calyptridium as you will find Cistanthe. The latest version of the Jepson Manual (California), the Oregon Flora project, and the WTU herbarium in Washington (linked above) all use Calyptridium.