There main difference between the four different ways of stopping/restarting are what does the main process do about its threads, and about itself.
Note that Apache recommends using apachectl -k as the command, and for systemd, the command is replaced by httpd -k
apachectl -k stop or httpd -k stop
This tells the process to kill all of its threads and then exit
apachectl -k graceful or httpd -k graceful
Apache will advise its threads to exit when idle, and then apache reloads the configuration (it doesn’t exit itself), this means statistics are not reset.
apachectl -k restart or httpd -k restart
This is similar to stop, in that the process kills off its threads, but then the process reloads the configuration file, rather than killing itself.
apachectl -k graceful-stop or httpd -k graceful-stop
This acts like -k graceful but instead of reloading the configuration, it will stop responding to new requests and only live as long as old threads are around. Combining this with a new instance of httpd can be very powerful in having concurrent apaches running while updating configuration files.
Source: https://httpd.apache.org/docs/2.4/stopping.html
Recommendation: Use -k graceful unless there is something wrong with the main process itself, in which case a combination of -k stop and -k start or -k graceful-stop and -k start are the options of choice.