Sun corals / Cup Corals are popular generic names used to describe dendro/tubastraea like corals. Sometime we attach a colour to describe the coral more fully but colour (for the most part) is not a unique species characteristics. You can have orange, yellow and even reddish tubastraea coccinea. Foods/ph/water chemistry and temperature (or even genetics) may be reasons for colour differences.
There are over 70 species in the dendrophyllia genus - most of which I'm sure we haven't seen in the trade. So there definitely can be white "sun corals".
The 2 photos you posted - the one on the left looks like a white variety of an arbuscula (could even be an altogether difference species) and the one on the right looks like it could be a variety of the many japanese sun corals - (hardly traded here) or even a balanophyllia sp.