I am getting confused about the definition of a "glass transition".
I read for example that it can be a transition from a rubber state to a brittle state in polymers. In this case therefore I would consider that as a "amorphous solid $\rightarrow$ amorphous solid" transition, since liquid polymers are not involved.
I read also that supercooled liquids can undergo a glassy transition, for example water can enter a glassy state. In this sense I would call it a "liquid $\rightarrow$ amorphous solid" transition.
Are these both "glass transitions" ?
I read that "glass transitions" are accompanied by small structural changes that cannot easily explain the difference (order of magnitutes) of physical properties between the two states. I can understand this problem in case (1), but in case (2) a liquid and an amorphous material to me are clearly very different (in one atoms diffuse, in the other not). So this makes me wonder if a transition of type (2) is still considered a glass transition or not.