For a long time the CLR came in 'regular' and 'client' versions, where the 'client' version was a subset that didn't include server-type namespaces. There was also a Silverlight variant. These were pretty similar to the various JRE distributions, if you're more familiar with the Java ecosystem.

A year or two ago Microsoft decided to get rid of the subsets because they didn't make sense anymore; "client-server" gave way to "distributed mesh" and it became perfectly reasonable for desktop application to expose a web service port in order to communicate with other apps.

'cloud-optimized library' sounds like a return of the subset idea, but going in other direction. It surely doesn't contain any of the WPF stuff that's used for creating desktop applications. It probably lacks other namespaces that are unlikely to be used in server applications too. I just hope they didn't cut too much out so that it's only usable for MVC/WCF/WebAPI servers. If I want to write my own low-level socket-based service, I hope I will be able to do that.

I think he is referring to running different versions with different CLRs side-by-side. It means Platform-as-a-Service friendly. Since in PaaS you usually don't own the machine, you just run code somewhere. You don't want to be tied in with is framework X installed on the machines or not. You want to be able to pull in what ever framework you like, as you would do with node.js for example

I think "cloud-optimized" means "vaporware".