The primary purpose of OS X's
open command is to open a file in the associated application. The equivalent of that on modern non-OSX unices is
xdg-open doesn't have an equivalent of OSX's
open -a to open a file in specific application. That's because the normal way to open a file in an application is to simply type the name of the application followed by the name of the file. More precisely, you need to type the name of the executable program that implements the application.
Linux, like other Unix systems (but not, as far as I know, the non-Unixy parts of OS X) manages software by tracking it with a package manager, and puts individual files where they are used. For example, all executable programs are in a small set of directories and all those directories are listed in the
PATH variable; running
sublime_text looks up a file called
sublime_text in the directories listed in
PATH. OS X needs an extra level of indirection, through
open -a, to handle applications which are unpacked in a single directory tree and registered in an application database. Linux doesn't have any application database, but it's organized in such a way that it doesn't need one.
If running the command
sublime_text shell doesn't work for you, then Sublime Text hasn't been installed properly. I've never used it, and apparently it comes as a tar archive, not as a distribution package (e.g. deb or rpm), so it's possible that you need to do an extra installation step. It's really the job of the makers of Sublime Text to make this automatic, but if they haven't done it, you can probably do it yourself by running the command
sudo -s …/sublime_text /usr/local/bin
… by the path where the
sublime_text executable is, of course.
open command you encountered is an older name for the
openvt command (some Linux distributions only include it under the name
openvt command creates a new virtual console, which can only be done by root and isn't used very often in this century since most people only ever work in a graphical window environment.