Your theory is pretty on point. A lot of higher end speaker manufacturers
give you a choice of titanium or silk tweeters in their component sets due
to their different characteristics. Silk dome tweeters are known to be a
bit
more smooth but not as bright and harsh. Titanium on the other hand is
very
metallic sounding and bright. It is a good choice if you listen to a lot
of
rap. Silk dome is more suited for softer music types like classical.

This isn't off the mark, but let it be known that it's just a
generalization. Not true all the time.

But
there are other kinds too, neodymium,

That's not a cone/dome type.

titanium alloys, even layered cone
tweeters.