I have owned both kinds.
There are a few names for these.
They are both porcelain crabs. Both are completely reef safe. Both get most of their food by grabbing particles out of the water with their 'fans' instead of their claws. Claws are mostly just for defense (or offence if he wants to drive away a clownfish) or grabbing large pieces of food.
The blue/orange one on the left is usually called a spotted porcelain crab (Petrolisthes galathinus).
The white and red/brown one on the right is normally just called a porcelain anemone crab (Neopetrolisthes ohshimai).
It is very common for the porcelain anemone crabs (white one on the right) to host in anemones. I had one that went straight in my LTA. They usually pair up very nicely and you can have a pair inside your anemone. Very cool to see. Sometimes they even get along with the clownfish and you can have a pair of clowns and a pair of porcelain anemone crabs. This did not work out too well for me, my aggressive gold stripe maroons drove away the crab.
I also had 2 spotted/blue porcelain crabs. They completely left anemones alone and were in the rockrock. The spotted ones will most likely not host with the anemone, but it will in no way harm it or any part of your reef.
Both porcelains are one of the few completely reef safe crabs imo.