The previous answers seem all to be a little confusing or incomplete, so here is a table of the differences...

+----------------+-----------------+----------------+----------------+
|    Command     | Displays Output | Can Get Output | Gets Exit Code |
+----------------+-----------------+----------------+----------------+
| system()       | Yes (as text)   | Last line only | Yes            |
| passthru()     | Yes (raw)       | No             | Yes            |
| exec()         | No              | Yes (array)    | Yes            |
| shell_exec()   | No              | Yes (string)   | No             |
| backticks (``) | No              | Yes (string)   | No             |
+----------------+-----------------+----------------+----------------+

• "Displays Output" means it streams the output to the browser (or command line output if running from a command line).
• "Can Get Output" means you can get the output of the command and assign it to a PHP variable.
• The "exit code" is a special value returned by the command (also called the "return status"). Zero usually means it was successful, other values are usually error codes.

Other misc things to be aware of:

• The shell_exec() and the backticks operator do the same thing.
• There are also proc_open() and popen() which allow you to interactively read/write streams with an executing command.
• Add "2>&1" to the command string if you also want to capture/display error messages.
• Use escapeshellcmd() to escape command arguments that may contain problem characters.
• If passing an $output variable to exec() to store the output, if $output isn't empty, it will append the new output to it. So you may need to unset($output) first.