Are both of these accounts listed in your Address Book? If so, try removing them.

I get a few messages that I send to newsgroups which behave like yours, saying they were sent from another of my accounts. It seems that sometimes the address book is searched for my name and comes up with the first account it discovers.

re :email from account A to account B, the received message in account B tells me it is "from" and "to" account B.

In addition to good advice from Zenos:

Your FROM email address may say account 'A', but if you sent it using the SMTP server for account 'B', then all your outgoing mail is actually using the B account email address.

Suggest you check the following: As you have two mail accounts, they will have different email addresses (user names) and different passwords. The rest of the server setting may be the same or different. However, you should ideally have one outgoing server smtp for each mail account/email address.

Right click on mail account in Folder Pane and select 'Settings' This will open 'Account Settings' window.

Bottom of left Pane: Click on 'Outgoing server (SMTP)' see first image below. Select the first outgoing server listed to see details below. Click on 'Edit' The 'User Name' = email address; will tell you which account should be using it. EDit the 'Description' field to something abit more useful for identification purposes eg: Personal or Work or email address. click on OK

select the other outgoing server in list. click on 'Edit' the User name' should be for the other mail account. EDit the 'Description' field to something abit more useful so you know it is different from whatever you set for the other SMTP. click on OK

Now make sure the mail accounts are using the correct smtp servers. Select the first mail account name in the left pane. bottom right will show which outgoing server it should use. Outgoing server (SMTP): select from drop down selection, the one whose description is for that mail account.

then do the same for the other mail account.

when both mail accounts are using the correct outgoing server. click on OK to close and save.

Exit Thunderbird and wait a few moments for background proceses to complete. Start Thunderbird.

Send an email from account A to account B. Report back on results.

Thank you to Zenos and Toad-Hall for your help.

I tried Zenos's suggestion first and looked at the address book. In the email column I found account A email address - and across in the Name column was account B email address! I selected Edit Contact for this row and found that for account A email address, the Display was account B email address! I replaced the Display entry with account A email address and now - mystery solved.

Thanks again to you both.