I know how these chords are made; and their structure in terms of intevals as well.
I even know how to play those chords all over the fretboard.
My question is. How in the world four different type of chords have the same name?
For those who don`t know what I`m talking about, I`ll list the chords in a generic way:

Alt=[1,3,5b,7b,9#]
Alt=[1,3,5b,7b,9b]
Alt=[1,3,5#,7b,9b]
Alt=[1,3,5#,7b,9#]

Can somebody explain this?
Thanks in advance.