It is clear from you edit that the second script is called enigma2.sh, and that you call it by writing enigma2.sh on the command line. The script is somewhere in your path (you declare that it is at /usr/bin/enigma2.sh, and I shall assume that /usr/bin is in your PATH variable). Combining that the script could be found (in the PATH) by the shell and that the first line of the script is #!/bin/sh, the kernel will start a new process that has a command line of:

/bin/sh enigma2.sh

You can confirm this by simply making the first lines of that script as this:

#!/bin/sh 
ps ax|grep enigma2
exit 0
...

You don't need to erase the script, just place the lines shown above at the start of the script and leave all the rest below.

Run it to get:

$ enigma2.sh
 3109 pts/6    S+     0:00 /bin/sh enigma2.sh
 3111 pts/6    S+     0:00 grep enigma2

There are two processes that include the word enigma2.

That explains part of the problem. Now, if you change the script to:

#!/bin/sh 
enigma_pid=$(ps ax|grep enigma2)
echo "$enigma_pid"
exit 0
...                     # leave the old script below (no need to erase it).

And run it:

$ enigma2.sh
 3509 pts/6    S+     0:00 /bin/sh ./enigma2.sh
 3510 pts/6    S+     0:00 /bin/sh ./enigma2.sh
 3512 pts/6    S+     0:00 grep enigma2

When you use a $(…) one additional process appear.

Removing the grep process with grep -v grep leaves 2 processes.

That is the number you get 2.

Note: Please, don't use uppercase variable names, those are reserved for environment variables.
Don't use ENIGMA_PID

Solutions

• First: If you are going to identify a process by its name, don't use the exact same name in other programs or scripts. You may call the script enigma33.sh.

• Second: In this case, you can restrict grep to match a name that ends at 2. The script ends in .sh and won't be counted. Use

   grep '[e]nigma2$'
  

And, since all you need is the count of matching lines use (-c):

enigma_pid=$(ps ax | grep -c '[e]nigma2$')

Yes, no need for grep -v grep since the regex [e]nigma2$ can not be equal (as an string) to enigma2.

Edited script:

#!/bin/sh


# Detect If enigma2 is running.
enigma_pid=$(ps ax|grep -c '[e]nigma2$')
echo "$enigma_pid"    

# Deetct if minisatip is running.
mini_pid=$(ps ax|grep -c '[m]inisatip$' )


# Check if the no_enigma file exists
if [ -f /home/root/no_enigma ]; then
    if [ -z "${enigma_pid##*[!0-9]*}" ] ; then
       echo "error: Not a number" >&2; exit 1
    else
        echo "It IS a number"
    fi
    
    if [ "$enigma_pid" -gt 0 ]; then
        echo "$enigma_pid"
        echo "enigma2 is running"
        killall -r '[e]nigma2$'           # make killing more restrictive
    else
        echo "enigma2 is not running"
    fi
    # Check if minisatip is running already, if not then start it
    if [ "$mini_pid" -gt 0 ]; then
        echo "minisatip is already running"
    else
        echo "minisatip is not running"
        echo "starting minisatip"
        /usr/bin/minisatip --satip-xml http://127.0.0.1:8554 -R /usr/share/minisatip/html       
    fi
else    
    # The no_enigma file does not exist
    # Check if minisatip is running, if yes then kill it
    if [ "$mini_pid" -gt 0 ]; then
        echo "minisatip is running, killing it now"
        killall minisatip
    else
        echo "minisatip is not running"
    fi  
    # Check if enigma2 is running already, if not then start it
    if [ "$enigma_pid" -gt 0 ]; then
        echo "enigma2 is already running"
    else
        echo "enigma2 is not running"
        echo "starting enigma2"
        /home/root/run_enigma.sh            
    fi
fi