iPhone Notes app - driving me crazy

I am trying to use the Notes application more. However, when I modified a saved note, the original note reappears or overwrites the data. When I click DONE, it looked saved with all the modifications.

When I look at the list of the notes, the one I modified shows different times and I do not know how to access the modified note.

Also, when I deleted a modified note, the original note appears. How does the notes app work? How can I access the modified notes? Is it a write once and save once program? Or are there multiple notes I just can't access?