Email synchronisation between iOS devices and Mac

Adding an email account on my Mac in Apple Mail does not add the same email account to iOS Mail.

Example: I add my work email to my iPhone using the normal iOS Mail app. When I open Mail on Mail on my Mac, my work email is not present. (I have tried it both ways - behave - and neither works).

I do not have iCloud Mail sync turned on in iCloud settings. I do not want, nor require a @iCloud email address. If I attempt to turn on iCloud Mail, I am asked to setup an iCloud Mail account before preceding.

Is there any way to synchronise my pre-existing email accounts in iOS Mail with my Mac?