Depends on how each client is set-up, they should both be setup as IMAP accounts, where all your e-mail stays resident on your ISP's email server and your clients/devices just sync the email from what's present on their. Now if one client deletes an e-mail then it will sync with the other device and remove it from there as well.

You have to see your sync settings and how long they are left on the server etc... if there is emails you never want to loose you can move them to a local folder on your computer.

So yes if you delete an e-mail from one the device, the next time your other device syncs up it will be removed over there too (unless you customize on how they interact)

POP3 acounts generally don't leave mail on the email server and delete them as soon as they are downloaded to your client, which was fine in the 90's when families shared one PC, but now, as you may guess isn't very good if you have multiple devices...

Yes, it does answer my basic question and thanks for that. I just want to keep the conversation alive re the strange to me at least statement in the Support general guide "must delete also from the server." Most likely just poorly expressed?

Google POP is IMAP and learn how they work. They are email standards not something Thunderbird dreamed up.

Guess just poorly worded as there are many exceptions to the rules as you can tell from all those options you can play with. You can almost make POP act like IMAP now a days if you were up fot the challenge haha. But generally POP was meant to always delete mail from the server once recieved, so in the early days you had to check your mail often or your mailbox at your ISP could fill up and you would loose mail :P