But is the ban permanent after the first offense? Even if it is, I always think there is some right to appeal. Either way, that's not the subject of this topic.
Yes. You will be permanently banned if you make a plagiarized post and the appeals are very unlikely to be accepted. Temporary ban is usually issued for spamming.
We have exceptions. There were many who were given a second chance and unbanned with the condition that they can not participate in signature campaign. Their signature space is disabled for a year or two. I don't know the gravity of the offense OP did but if it is slightly tolerable then a signature ban can give him a time for redemption.