It is confusing and people sometimes refer to the private Owner Key as the "password" for the regular Owner key which is one of the sources of the confusion I think!
The method of signing up has also changed which I suspect may be adding to this - there may have been an extra password when people signed up using Facebook or other accounts - I honestly don't even remember now.
The last time I changed my keys was a few months ago and I only got one "master" key which I presume is the private Owner Key but there is no way to check now since you cannot view it (private owner key) anymore.
If I am wrong I am happy for someone to correct me.
Anyway the point is that whether you have a Private Owner key or Master Password, these should be kept offline unless you really need them and the only situation for that would be to change all the other keys.
For day to day use people should only use the Posting key.