One additional difference between GMail/AppleMail "conversations" and Thunderbird/Evolution "threading" is that the formers do merge conversations from different IMAP folders (as long as the auto-threading rules kick in), and do merge duplicate mails automagically (e.g. if you have the same mail in "Sent" and in "Mailing List Foo", they will not be displayed twice in the conversation). This for instance allows to have full conversation for emails in Inbox, which is usually not working in Thunderbird since the emails are usually split between Inbox and Sent.

IOW, a "conversation" is displayed in any folder that contains at least one message which is part of it, and contains all messages that are logically part of it, even if they're not stored in that folder. A "thread" is a visual arrangement of the emails in the specific folder, but doesn't cross the folder limits.

Another important point of the user interface is the "mute" button, that hides (archives) the conversation and doesn't allow it to popup anymore even if new messages arrive (in any folder).

I believe it means "flat" threaded email. You care about all messages that are part of a conversation, but you are not concerned about the exact structure of a conversation, so you list all messages of a thread in time-received order.

That is what I was afraid of. It did not make any sense to me why one would advertise to the HN crowd that even though the mail client may not provide the best threaded message display at least it does not provide the worst case scenario of flat sorted by date emails. I really wanted to like mailpile, but the email threading is terrible for serious use with mailing lists.

It means conversations really similar to gmail conversations

BTW. gmail has flat conversations, threads usually have more hierarchy.