On 22/10/2020 11:33, R D S wrote:
Can somebody tell me...

Our web host had us using (for example) mail.bobsserver01.co.uk for
email server settings whereas Thunderbird et al autodetects
mail.ourdomainname.co.uk
Both seem to work equally well.

But when they move us to a different server (no idea, but it's at least
annually) I need to go around several PCs changing several email
addresses to mail.bobsserver03 etc.

I asked in the past and it was suggested their way was better with no
explanation but i've asked again today (we've moved again, shrug) and
they've conceded that it's fine to use mail.ourdomainname.

What, if anything, is the difference?

mail.ourdomainname is probably an alias for one (or more) of their
physical servers. One level of indirection won't hurt at all.

The advantage is that it should redirect if they get taken over by Cate.

--
Regards,
Martin Brown