Official from PHP.net 5.6 - 7.1 is end of life.
5.6.x support ended on 01 Jan 2019
7.0.x support ended in Jan 2019.
7.1.x support ended in Dec 2019.
7.2.x is currently on security fixes only which appears to end Dec 2020.
7.3.x is actively supported until 06 Dec 2020. Then goes to Security only fixes until 06 Dec 2021.
7.4.x is actively supported.
source: https://www.php.net/supported-versions.php
The jump from 5.6 to 7.x brought large speed improvements to PHP and a large number of changes.
While osTicket currently supports 5.6 they are developing and upgrading the code to be optimized for 7.3 currently.
Yes they are probably both running fine.