How to run remote applications on OS X like X11 does? Is there any application that can be installed in OS X (Lion) that will allow a person to run applications from the host system on a guest system, displaying only the windows for the application? In other words, can Cocoa applications display their windows on another OS X Desktop than the machine on which they are running?

X11 allows you to run an application remotely without sharing the whole Desktop.

I am currently using VNC (Screen Sharing), but because of screen resolution differences, it isn't ideal.
Short answer is no. 

Cocoa is not designed as a remote procedure call (RPC)-esque protocol, while X is. You cannot tunnel the interfaces of Cocoa applications like you know it from X11 natively, only using protocols like VNC that transfer the actual bitmap rather than the rendering instructions.

On the other hand, you are able to use remotely running X applications via SSH.