MySQL startup programs | mysqld | mysqld_safe | mysql.server | systemd

MySQL Server and Server-Startup Programs:

• mysqld — The MySQL Server
• mysqld_safe — MySQL Server Startup Script
• mysql.server — MySQL Server Startup Script
• mysqld_multi — Manage Multiple MySQL Servers

mysqld:
mysqld known as MySQL Server, is the main program that does most of the work in a MySQL installation. The mysqld program has many options that can be specified at startup. 
Explore option using command:
shell> mysqld --verbose --help
Initialize mysql daemon:
mysqld  --defaults-file=/etc/my.cnf  --initialize &
Typical config file:
[mysqld]
socket=/mysql/<db_name>/data/<db_name>.sock
port=3350
pid-file=/mysql/<db_name>/data/<db_name>.pid
basedir=/mysql/<db_name>/data
datadir=/mysql/<db_name>/data
user=mysql
tmpdir=/mysql/<db_name>/temp
slow_query_log= on
slow_query_log_file=/mysql/<db_name>/logs/<host_name>-slow.log
log-error=/mysql/<db_name>/logs/<db_name>.err
mysqld_safe:
Oracle recommend mysqld_safe to start a mysqld server on Unix. It adds safety features such as restarting the server when an error occurs and logging runtime information to an error log.
Note: For some Linux platforms, MySQL installation from RPM or Debian packages includes systemd support for managing MySQL server startup and shutdown. On these platforms, mysqld_safe is not installed because it is unnecessary. Most of the options to mysqld_safe are the same as the options to mysqld. Always use mysqld_safte with --defaults-file option first otherwise it will not work.
mysql> mysqld_safe --defaults-file=file_name --port=port_num
The mysqld_safe script is written in such a way it start a server which is installed from either a source or a binary distribution of MySQL.
Explore more about mysqld_sfae at :
https://dev.mysql.com/doc/refman/8.0/en/mysqld-safe.html
mysql.server:
mysql.server script is available for Unix and Unix-like system, which starts the MySQL server using mysqld_safe. It is also used by the macOS Startup Item for MySQL.
For some Linux platform, when you install MySQL using RPM or Debian package it includes systemd to manage MySQL server startup and shutdown. For these platform mysqld_safe are not installed as they are unnecessary.
shell> mysql.server start
shell> mysql.server stop
mysql.server changes location to the MySQL installation directory, then invokes mysqld_safe.
To start and stop MySQL automatically on your server, you must add start and stop commands to the appropriate places in your /etc/rc* files mysql.server reads options from the [mysql.server] and [mysqld] sections of option files.

Explore - https://dev.mysql.com/doc/refman/8.0/en/mysql-server.html
mysqld_multi:
mysqld_multi is designed to manage several mysqld processes that listen on different Unix socket files and TCP/IP ports. It is used to start, stop, or report the status of mysqld.

Note: For some Linux platforms, MySQL installation from RPM or Debian packages includes systemd support for managing MySQL server startup and shutdown. On these platforms, mysqld_multi is not installed because it is unnecessary.
https://dev.mysql.com/doc/refman/8.0/en/mysqld-multi.html

shell> mysqld_multi [options] {start|stop|reload|report} [GNR[,GNR] ...]

systemd:
systemd is the System Management Daemon
•systemd provides standards for controlling the Linux boot process
•systemd is intended to replace init start-up scripts for boot process
•systemd is integrated process monitoring and automatic restarts in the event of a service failure/termination
•Starting with MySQL 5.7.6, process monitoring and auto-restarts are now handled by systemd on systems that have it
•If mysqld fails due to a restartable failure like a crash, then systemd automatically restarts mysqld
•multiple services are able to start at same time, improving boot times
•You can pass other custom options to mysqld by creating additional entries/lines in /etc/sysconfig/mysql using the MYSQLD_OPTS=”option” format
•You can also specify custom options and environment variables using the systemctl command:
•$ systemctl set-environment MYSQLD_OPTS="--general_log=1"
The custom options can also be unset using:
•$ systemctl unset-environment MYSQLD_OPTS
•mysqld.service: This is the systemd service definition file that tells it what service to start, specifies auto-restart settings, type of service it is and all of the dependencies between various units, etc.

Ref. : https://mysqlserverteam.com/mysql-5-7-native-systemd-support/