Where are you seeing those?
"Biz" may refer to a Top Level Domain, like .com, but it's .biz
"Dreamhost PS" is their line of Private Server services. As opposed to Shared Hosting with a large pool of users, you can have VPS, which is a Virtual Private Server with your very own allocated resources. There are other users on the server with the slim potential to torpedo your performance, but generally, it's quite good. There's also Dedicated Server (quite expensive) which is a rack mount server with only your account on it.