There’s plenty of tonal variation within each of these groups. I’m not sure I agree that what a recorder maker would regard as a narrow-bored cylindrical instrument would be heard as fundamentally different from a cylindrical wooden instrument produced by a whistle maker. It’s easier to speak categorically about differing characteristics if the comparison is between metal whistles and wooden recorders. A large part of that lies in the difference between the thickness of their walls. The greater it becomes, the more the internal geometry of the toneholes becomes a manipulable and audible factor. It also maps into how the instrument can be voiced. As demonstrated by the Susato, this is the overriding factor.
The difference between the sounds of recorders and whistles is minuscule compared to the variation among organ pipe stops made on the same basic principle. They are referred to as flue or labial pipes, and are grouped in three tonal families. The first consists of the principals (aka diapasons) that largely determine the characteristic pipe organ sound. The other two are flutes and strings, abounding with stops intended to emulate orchestral and other instruments. Blockflöte (German for recorder) and Flageolet are commonplace and I wouldn’t be surprised if there was a Tin Whistle or two out there. Although made on the exact same principle, there are string stops that only an erudite ear would recognize as flue pipes.
One of the differentiating factors is the gross geometry of the pipe. Two of the primary forms are open cylindrical and conical tubes. These also figure in the answer to your question about the diff between recorder and whistle sounds, as well as differences within the respective groups. Organ pipe makers additionally characterize stops by the ratio between the circumference of a pipe and the width of its mouth (what we’d call the window). The ratio between the width and height of the mouth is another main scaling factor. From there on everything is a matter of how the pipe is voiced, which is equally germane to the distinctive sounds of tin whistles and recorders. (There’s a good intro to how flue pipes are voiced here.)