During a standard SAP HANA database system installation, the SYSTEM user is a crucial database user that will be created to handle administrative tasks within SAP HANA. The sapadm user is another important user created during installation to manage operating system-level functions and administrative tasks related to SAP HANA. The SAP<SID> user is also a necessary part of the installation for distinguishing between different instances, but the <sid>crypt user is not a standard part of the installation process.