Linux Process Automatically Starts Again with New New Pid After Killing

You are misunderstanding the output of ps. Your first command, sudo systemctl stop nginx is the right way to stop a running service and did actually work. The line you see in the ps isn't a running nginx process, that is the grep process you launched:

$ ps aux | grep foo
terdon    642773  0.0  0.0   8944  2384 pts/23   S+   13:40   0:00 grep --color foo

When you run ps | grep, that is a process so that is also included in the output of ps. And, since your grep contains the string nginx, the grep itself is included in the output of grep. The usual ways around this are:

1. Use pgrep instead of grep

    pgrep nginx
   

   That will only return anything (a list of PIDs) if there is a running nginx process.

2. Use a character class in grep so that you can still match the process, but will ignore grep itself:

    ps aux | grep '[n]ginx'
   

Because the grep process now contains [n]ginx instead of nginx, it will not be matched by itself.

Since these are set up as services and, presumably, set to launch automatically, killing them just makes them restart. To stop them, you should always use systemctl stop nginx or, if your system supports it service nginx stop.