There are 2 kind of corks made of cork: the cilindric ones, used for non sparkling wines, and those made of a lower cilindric part and an upper, larger, dome shaped part that's the part one grabs to open the bottle. The latter are used for sparkling wines, as is champagne. Usually the lower part is made of good cork whose quality maxes at the bottom end (the one in contact with the wine) and decreases while climbing up towards the upper part of the cork, which is made of minced and glued low quality cork bits. In Italy, these 2 parts corks are called "tappi a fungo", which translates to "mushroom corks": what are theyr english and french name?
As a consumer on the west coast of the US, I can definitivly say we call them "corks". :-) In my experience, the US/Champagne joint ventures all use large corks which are the same all the way through. If you let them sit for a couple of days after opening the wine, they will expand to have relatively straight sides. While I've seen the composite corks you describe, I've never heard them called anything other than "corks."
The bulk of sparkling wine corks (stoppers) are manufactured cylindrical. They are then only partially inserted into the bottle. That part which remains outside of the bottle tends to expand towards it's original size. But this is also constrained by the wire hood. These factors account for the mushroom shape.
The body of the stopper is indeed made from "grain", granular pieces of cork which are strictly controlled and bonded together with an adhesive. This is called an "agglo", as in agglomerate. Make note that this is not an economic technique as with cheap still wine corks. It is a structural one. "Natural" (one piece)cork would be totally inappropriate for sparkling wine. On quality sparkling wine corks there are 1 or 2 disks glued to the end of the agglo body, and in touch with the product. The quality of these discs, and whether there are 1 or 2 of them, is the real measure of the quality of the stopper. There are other important nuances to their manufacture, but suffice it to say that they are seriously engineered for performance. They must stay in the bottle (not be "fliers" which can cause injury), but must be removable lest consumers try to use a tool to extract them (also dangerous). Some manufacturers extrude the agglo bodies in sticks, and cut them to length. The better ones form them in individual molds - much more expensive, but better physical dynamics. Coatings are critical. QC is exigent.
I can't speak about the 17th century, but prior to the age of mechanization (not all that long ago, in Portugal), I believe that cork bark for sparkling wine was hand cut into sheets, laminated together, then the stopper carved from those laminated blocks. For a wine under pressure, the rings of the cork bark need to be at right angles to the pressure. This is not the case with still wine corks. If you look at the ends of a natural still wine cork, you can usually discern the tree rings. The discs that are now glued on the end of a Champagne cork are cut parallel with the tree rings. It's a little harder to see, but the rings would be visible on a sparkling cork disc from the side. They are less permeable this way. The finest stoppers may even have 3 of these discs glued to the end. Very expensive. The finest quality cork bark is reserved for the discs for sparkling wine corks. If you want to get into some of the minutia of cork, check out the Cork Quality Council website. The CQC is an industry association dedicated to educating wineries & consumers about natural cork. It was actually formed in order to compel the cork producers to address the TCA problems relating to natural cork, and to help the wine producers develop quality control procedures and good corking practices. It's a little off topic (not much on sparkling wine corks), but interesting for those who wish an understanding of natural wine cork.
I think it's an economic phenomenon. Finally the Portuguese wine producers are getting the respect, and achieving the quality, that may have eluded them for so long. In other words, they are making better wine, getting higher prices, an can afford the better quality packaging materials. Currency exchange has an effect, as well. Quality cork goes to the highest bidder, be you Portuguese, Italian, Ozzie, ......
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