both "Sent Items" and "Sent Messages" appear in Outllook after using Mail

Your answer is what I already knew was true.

What I didn't know about Mail's message handling was that Outlook doesn't recognize messages send from Mail and Mail doesn't recognize messages sent from Outlook.

Messages sent from home using my work account in Mail show up in the work account mailbox under Sent, but NOT in the Sent Items folder under my IMAP work folder. When viewed at work, those same messages show up in a Sent Messages folder in Outlook.

Messages sent from work using Outlook show up in Outlook in the Sent Items folder. When viewed at home, those messages are NOT in the work account mailbox under Sent, but they are visible in the Sent Items folder under my IMAP work folder.

So, as I'd said, sent messages end up in two different folders depending upon whether they were sent from home or from work. I guess that's due to the different way that Mail and Outlook file sent messages. And I'll have to get used to looking in two different folders when searching for an old sent message, it appears, unless there's some trick for changing where those two applications store their sent messages.

I guess that's what I was trying to ask in the original post.