They are both sent to a specific person unless you include additional users. They are both a private means of communication up to the point that someone makes them public.
A private message on the other hand has the expectation of privacy.
Private or personnel message is just a name for the forum messaging feature. I would agree with you if the forum had both private and personnel messages. In that case, we would need a way to distinguish those two.
What if the on-forum messages were called Bitcointalk forum messages without mentioning the terms private or personnel? How are we supposed to look at them then?
Perhaps I should have written that there is no *reasonable* expectation of privacy for a personal message.
The current implementation of the PM system makes this clear. For example, it is trivial to Blind Carbon Copy a third party any PMs that you send, including when you include a quote of a PM you previously received.
I would say, in general if you need to use some kind of encryption key (such as your GPG key) to read a message, there is an expectation the message will stay private. If the message can be read without using any kind of encryption key, there is no (reasonable) expectation of privacy. Exceptions to the above would be if the parties agree ahead of time.
When you encrypt (or decrypt) a message with GPG, you know exactly who can read a particular message.