Actually the term "woodwind" is one you have designated in your time for all pipe instruments in which the covering and uncovering of holes by movements of the fingers constitutes the primary means of making the notes of the scales. I have grouped our Renaissance instruments according to your terminology to make it easier for you to understand. The material of the pipe may be ivory, metal, glass, etc, though for most types the traditional material has been wood and makers generally serve their apprenticeship as wood turners.
The way to make a sound with these instruments provides an additional way to group them:
By blowing a jet of air onto a sharp edge provided by the instrument, as in recorders and flutes:
Elizabeth on the Flute (sample sound included) Addame on the Recorder (sample sound included) By causing the airstream to set in vibration a "reed" made from natural cane cultivated for reed-making purposes in the South of France and elsewhere, as in the case of crumhorns, shawms, bagpipes, etc.:
Sol on the Crumhorn (sample sound included) Elenore on the Shawm (sample sound included) William on the Glastonbury Pipe (sample sound included) Brian on the Bagpipe Morgana on the Racket Shelby on the Curtal
There are also pipes which are fingered as other pipes but are sounded like brass instruments by vibration of the player's lips across a mouthpiece cup. Such are the cornett and the serpent and they can also be classed with the brass instruments.
References:
Hadley, Benjamin, ed. Britannica Book of Music. Garden City, New York: Doubleday & Company, Inc., 1980.
Hindley, Geoffrey (ed.). The Larousse Encyclopedia of Music. Excalibur Books, New York, 1982.

