It’s always a delight to know something about a subject and suddenly to have its context expanded.
All flutes work in the same way, with a stream of air generating sound energy by flowing over a sharp edge and thus shedding vortices. The two families of flute are the transverse flutes, such as the orchestral flute and the military fife, and the fipple flutes, such as the recorder and the South American quena.
In transverse flutes, the sound generation is controlled by the player’s embouchure directing the airflow at the far edge of the hole in the mouthpiece (the physics is much the same as generating a tone by blowing across to top of a bottle). In a recorder, the mouthpiece has a duct formed by the shaped gap between the main longitudinal hole drilled through the instrument and the fipple plugging the top end of it. The duct accurately directs air onto the sound generating edge, which is an aerofoil section at the bottom of the rectangular hole in the front of the instrument. (This is what makes the recorder so good as a beginner’s instrument; no embouchure required: just stick it in your mouth and blow.)
The interesting instrument from the etymological point of view is the quena (Wikipedia link with pic). This is a fipple flute with no fipple. The upper end of the instrument is just an open hole while the tone-generating edge is the lower edge of a U-shaped notch. You play it by resting the top of the instrument just below your mouth and blowing air so that it just catches the bottom of the notch. Tone and volume are controlled by the speed of airflow, embouchure and the configuration of your lower lip. (The quena has quite a wide bore for its size which, combined with the aerodynamically relatively inefficient sound generating edge, gives it the wonderfully breathy sound that typifies it.)
So a quena is a fipple flute with no fipple, but it seems that aldiboronti’s discovery in the OED explains why: the piece of anatomy that takes the place of the wooden fipple is itself called a fipple to a Northcountryman. This rather suggests that the term fipple flute harks back to a European forerunner to the recorder that was similarly open-topped.
At least two of my music books suggest an origin of the word recorder as meaning ‘keepsake’ (cf Spanish recuerdo), which assumes that recorders were once given thus and may well be complete hogwash. The musicological sense that the OED offers seems far more reasonable.
The German names for the two families of flute are Querflöte and Blockflöte. The former is obviously ‘cross-flute’. I had taken Block in the latter to refer to the wooden fipple, with Block as a noun in the sense of ‘plug’, but now I wonder if it’s actually a verb with the sense of ‘obstruct’. My German isn’t good enough to comment further and my knowledge of German etymology is zero.
[Edited to repair a typo.]