I think Leeneia was referring to a simpler point, which that a large proportion of the notes played by D whistle and C recorder have the same fingering (ignoring the thumb). I find it helpful to think of these common pitches (particularly the notes you get with the G and D fingerings) as reference marks when playing instruments in different pitches.

Not everybody going between the two instruments gets this at first. John Everingham at Saunders Recorders told me he nearly always had to tell customers asking to buy a C whistle that if they were coming from the descant recorder and wanted to play the same stuff, that wasn't what they really wanted.

The 'early recorder' (think King Henry VIII) is basically almost identical to the whistle, and was diatonic.

No it wasn't. Ganassi was contemporary with Henry VIII and his fingering system covers everything you can do on a standard modern recorder and a lot more. His treatise "La Fontegara" is downloadable for free (be warned it's a ghastly example of how make every conceivable mistake in technical writing). This is a Ganassi recorder in action:

Racheal Cogan playing Greek music with Ross Daly

You can also download a facsimile of Virdung's "Musica getuscht" (1511, when Henry VIII was 20) from IMSLP (IMSLP86312-PMLP176555-Virdung__Sebastian__Musica_Getutscht.pdf). Pages 108-109 give you a fully chromatic fingering chart for the recorder - it is somewhat whistle-like but there are crossfingerings. (I haven't figured that diagram out fully yet - it looks like a necromantic sigil and the explanation is in late mediaeval German - but there is no doubt about the chromaticism).