This makes no sense whatsoever.

Both my Macs in this office have the same Mail Preferences now: using the same server at one ISP to send and receive emails.

Having been away for a week, no one has changed anything, I now find that one Mac cannot send emails but the other one can and does. The settings are identical.

The error message on the Mac which won't send emails is something like "check your settings". I reported this to the ISP and their reply was polite disbelief.

I have therefore reinstated the previous outgoing mail server (which is a different ISP) on that particular Mac.

Crazy. Mad. Nonsensical, eh?