@Michael Durrant's answer ably covers the shell itself, but the shell environment also includes the various commands you use in the shell and these are going to be similar -- but not identical -- between OS X and linux. In general, both will have the same core commands and features (especially those defined in the Posix standard), but a lot of extensions will be different.
For example, linux systems generally have a useradd command to create new users, but OS X doesn't. On OS X, you generally use the GUI to create users; if you need to create them from the command line, you use dscl (which linux doesn't have) to edit the user database (see here). (Update: starting in macOS High Sierra v10.13, you can use sysadminctl -addUser instead.)
Also, some commands they have in common will have different features and options. For example, linuxes generally include GNU sed, which uses the -r option to invoke extended regular expressions; on OS X, you'd use the -E option to get the same effect. Similarly, in linux you might use ls --color=auto to get colorized output; on macOS, the closest equivalent is ls -G.
EDIT: Another difference is that many linux commands allow options to be specified after their arguments (e.g. ls file1 file2 -l), while most OS X commands require options to come strictly first (ls -l file1 file2).
Finally, since the OS itself is different, some commands wind up behaving differently between the OSes. For example, on linux you'd probably use ifconfig to change your network configuration. On OS X, ifconfig will work (probably with slightly different syntax), but your changes are likely to be overwritten randomly by the system configuration daemon; instead you should edit the network preferences with networksetup, and then let the config daemon apply them to the live network state.