But a link or a reply is not the same thing ?
No, they are not the same thing.
I frequently get pingbacks when people post “my favorite plugins” and include a link to one of my plugins. It’s not a direct reply, it’s content that includes a link to my page.
I would expect a trackback if somebody actually made a post that was a direct reply to one of my own posts. Like I posted something saying “Bush sucks!” and somebody else posted “Otto said Bush sucks! I agree and here’s why:”, then yeah, that’s a reply and a trackback makes sense.
do you see part of the mention/reply in the both case, or not ?
For a trackback, yes, the sending party sends a piece of their comment/post to the receiving site.
For a pingback, no, the sending party only sends the URL. The receiving site must go retrieve the content itself and get some piece of it if it wants to display it. WordPress does this, and displays a small portion of the content from the pinging site.
But there is a fundamental difference between somebody actively telling me something (via a trackback) and me going to find what they have to say (via a pingback).
As for “what you see”, well, that depends. WordPress stores all three as “comments”, but you can make it display them mixed, or separately. You can have it style them differently, you can choose not to display pings or tracks or comments or whatever you like. This is all up to the theme itself.