Running Reaper off external portable HD

I installed Reaper on my desktop computer and then went through the "install on USB or external hard drive" motions. Do I run Reaper from the external hard drive now to be able to take that hard drive to another computer? Does the other computer need Reaper installed on it too?

You can now run REAPER from the other hard drive. Your settings will also be copied and you'll basically be running REAPER portable.

When you say to install my plug ins, are those things that don't come with the Reaper program? I didn't install anything extra, just the main version of Reaper downloaded from the site.