signleton_methods / methods / public_methods - weirdness?

Hi!

I was trying to find out the "class methods" of some classes.
Looking in the PickAxe I found out that there are at least three 
methods that return almost the same thing for a class/module:

     Object#singleton_methods(flag)
     Object#public_methods(flag)
     Object#methods(flag)

So potentially we can get six (3 * 2) different results. To find out 
the difference between all invocations, I ran the methods on all 
builitin classes/modules, and compared the result. It turned out 
that I actually got 4 different results:

     - methods(false) and singleton_methods(false)
       give the same result

     - singleton_methods(true)
       gives a unique result

     - public_methods(false)
       gives a unique result

     - methods(true) and public_methods(true)
       give the same result

The PickAxe said that Object#public_methods was a synonym for 
Object#methods. This is apparently not true (or true only when the 
argument is "true").

To me it seem like these methods have "degenerated" into something 
that is almost impossible to explain. Neither the PickAxe nor the 
online-docs explains it in a way so I can understand the 
differences. Can anyone explain the logic behind these different 
methods and their results?

Maybe I'm just stupid :)

/Johan Holmberg