What is the difference between a glassy, amorphous and a vitreous phase?
After some reading I have decided to answer this question myself for anyone else with the same confusion. The info is from the downvoted answer of alphonse and the wiki-link, but with a better overview.


Both vitreous and glassy are amorphous. Amorhous is the broadest term to rule them all.


Some amorphous materials have a Glass Transition Temperature (GTT). Above this temperature the material becomes a viscous liquid. note that both below and above the GTT the material is amorphous.


An amorphous solid that has a GTT is called a glass.
The transition (heating) over the GTT results in a glassy phase.
The reverse transition (cooling) corresponding to the GTT is called vitrifcation. The result is a vitreous phase.


If I made mistakes please comment and I will update the answer.