Well the baize I use for my magic tables is definitely a felt. But there are many kinds of baize, snooker baize for example, also that used on card tables - quite different. In Victorian times it was stuck on doors as a sound proofer.
Sharks tooth is a weave, not particular to gauze, I've used several kinds over the years. The theatrical catalogues at one time would list at least a dozen different gauzes. Some were used to paint on, others were just to add haze. Sometimes multiple gauzes were hung one behind the other and then rapidly flown one after the other as the lighting change, giving an effect of a fog dispersing. Far more magical, to my mind, than today's obsession with smoke machines and carbon dioxide fog.
I have used gauze transformation effects on the marionette stage - but only few times. We used it with an underwater ballet, and also in a production of Macbeth. Then we used it in an illusion show on strings - not very successfully. Also we tried a gauze effect for the growing hedge of thorns in The Sleeping Princess - although we cut that scene out of later productions.
Because of the shallowness of the marionette stage it is extremely difficult to get the lighting right. Also it isn't easy to fly it after the melt through and you don't want to be stuck with it once it has served its purpose. Generally I found that on the puppet stage it was more trouble than it was worth.
But in the live theatre, in ballet and pantomime I have seen it used to wondrous effect.
Incidentally shark's tooth woven linen tape was said to be the best for swazzle use. I don't really think the weave made any difference to the sound. The weave might have an effect with a gauze though, in the way it refracted the light perhaps, or it might have been easier to paint? Did your source say why they preferred it for gauzes?