I believe cut just means the bicolor / split in the middle for this particular design.
As for wash, you can read about Hermes' description of it here :
https://www.hermes.com/us/en/story/168666-carre-wash/
Basically it's a process that Hermes uses on their regular silk that makes them machine washable, and also it does change the appearance as well as the texture of the silk. It makes the colors less vibrant / more muted, and the texture softer (some may find it easier to become wrinkled and some have said they don't think so). Generally speaking, this makes wash silks more casual than regular silk. If you see one in person IMO it's pretty easy to tell whether it's wash or regular silk.