The main confusion with the soft dome tweeters is the misunderstanding of terms.
SOFT simply means what it says, soft, as opposed to hard.
TEXTILE simply means fabric. Ie. the industry that deals with the materials used in clothing is known as the Textile Industry.
So the terms Soft, Cloth, and Textile are all basically interchangeable.
It gets a little varied after that.
SILK is the specific material used in a Soft/Textile dome.
If the material isn't specified then it could mean anything but is most likely either cotton or some sort of nylon derivative.
Of course, no textile material is airtight without the addition of some sort of sealing material.
This is where POLYAMIDE comes into play. It's the glue that seals the textile in a soft dome.
All softdomes can technically be considered MATRIX materials. Matrix simply means that at least two different materials are mixed for mutual benefit. Fiberglass and Carbon Fiber are common examples of matrix materials. They mix a hard polymer with a flexible but strong cloth-like material. The polymer gives the cloth functional rigidity while the cloth material (the actual carbon or glass FIBERS) gives the matrix it's strength.
So, getting even more complicated, you can see that Carbon Fiber and Aramid (early Focal type) tweeters are sort of quasi soft/hard tweeters. They are matrix by design, just like Soft dome. But they are also rigid, like hard dome.
And they share pros/cons of both types.
Metal dome tweeters are typically made up wholly of whatever material they claim to be. Though not always. When the first Beryllium tweeters came out, only Focal had the technology to form pure Beryllium. So all others where hybrids. Though now others have caught up and there are others with pure Beryllium domes. Before Beryllium was Titanium. Titanium is also difficult to work with, though not nearly as Beryllium. It is also not toxic like Beryllium can be. And before Titanium there was Aluminum. Aluminum is by far the easiest metal to shape, but it comes at the cost of rigidity.
The whole idea with tweeters is to basically have the material be infinitely rigid while being zero mass. So you start playing with the various properties of the material. Titanium is heavier than Aluminum, but it is also many times stronger. So you can use much less of it, thus bringing the overall mass down for a given stiffness. Beryllium is even better.
BUT, as most people notice, all of this metal stuff comes at a cost. That being ringing. But that's a whole other subject.......