hi laura, it's fine if you continue to use your current flash player 22 plugin. though they share the "esr" bit in the name, this version of the flash plugin isn't made especially for the firefox esr release - they just follow the same concept of only providing security but no functional updates to their product... and in addition, since adobe will soon cease to maintain its esr branch, it's better if you don't switch there.

The Firefox 45 ESR is basically Firefox 45.0 Release but in extended security updates support as last update version will likely be 45.8.0esr.