Every process will be listed in the output of ps aux; whether running, sleeping, zombie or stopped.

However, in your case, since you ran the process using sh abc.sh, sh is the application(shell) that is running and not abc.sh. Hence, ps aux will not contain the process abc.sh because of which grep could not yield any result.

So, the correct way you should have used it is as:

ps aux | grep sh

This may also return you other process that are running having the string sh anywhere in their output of ps aux.

You should note that the process will be "running" when the output of ps aux has its STAT as R. If it is something other than that, it is not running at the instance you fired the command to check the running processes. The different process states can be found in the man page for ps:

D    uninterruptible sleep (usually IO)

R    running or runnable (on run queue)

S    interruptible sleep (waiting for an event to complete)

T    stopped, either by a job control signal or because it is being traced

W    paging (not valid since the 2.6.xx kernel)

X    dead (should never be seen)

Z    defunct ("zombie") process, terminated but not reaped by its parent

You could as well run the top command to check if the process is running or sleeping and the amount of CPU, RAM it is consuming. (This will again list your process as sh).

However, if you do want your process to be listed as abc.sh, then you should have the first line of the script you are running as:

#!/bin/sh

so that the shell will know what application to use to run the script(sh in this case, change it to #!/bin/bash for bash) and then provide executable permissions to the process using:

chmod +x /path/to/abc.sh

replacing /path/to/ with the location of the abc.sh file and then run abc.sh using

/path/to/abc.sh

again replacing /path/to/ with the location of the abc.sh file.