It shouldn't stop at the end of the line - for that, press Shift+End. But I'm guessing you meant that you think it should stop at the end of the word.

Both phenomena you describe are the result of the same behavior. Pressing Ctrl+Right or Ctrl+Left jumps to the beginning of the next word in the relevant direction. This is the default behavior of the Tk Text widget, which I am liking less and less as time goes by. (issues with selections, 'end-1c', ...)

What you ask has already been suggested to me: that it might be useful, and perhaps more intuitive, to have Ctrl+Right jump to the end of words instead of beginnings.

I'll bring this up on the IDLE-dev mailing list as a possible feature.