It may be worth exploring the specifics, as the conversation is underway.
Don't reveal anything here that would allow others to read your posts and know who you are, however.
I sense that your concern here is how others might perceive you, based on the phrasing of the sentences regarding your termination. Rather than getting hung up on whether the word is "performance" or "conduct," perhaps it's better to explore what actually occurred, and how to move on from that.
For perspective, I've been around the industry a while. A long, long time, actually. In that time, I've seen the whole gambit, from rides that stopped when the student went more than 50' below MDA without disconnecting the autopilot, to students who returned to the hotel and beat up the instructor and tried to drown him in the pool. I've seen students who didn't recognize the problem, others who became deeply depressed over the matter, others who went straight back to the hotel, hit the books, rented a simulator, and came back and passed with flying colors, students who quit and never returned, and a few that had screaming meltdowns. I saw an entire class of upgrades fail and they all later claimed that they'd been the best class of upgrades to ever go through the program, and that they'd all have passed, if only they had one more sim session. It's very possible that each one of those events could have been described by the same language you're citing here...not all those events were unrecoverable. I've known a lot of pilots who had some event in their career from which they moved on and had very successful futures, too. A lot.
Simply because a company will not re-hire does not mean the person who has left is a bad prospect. I know companies that will not re-hire anyone who has left them, whether voluntary or involuntary. The devil, as they say, is in the details.
Let's get to know the devil.