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Difference between different types of Amorphous solids?

So I'm doing a research task about glass, its properties, structure, production, and economic impact, but am having a problem finding a distinct difference in definition between a plastic and a glass. Both are amorphous solids, right? Both undergo a glass transition phase, right? Like plastics don't melt, but rather get softer and harder with or without temperature, and so does glass, so what is the difference by definition? 

I read that all glass are amorphous solids, but not all amorphous solids are glass. Please explain how this is so, thankyou :)
gpt
Amorphous solids are solids which lack the long-range order of crystals.

Glasses are a subset of amorphous solids which show a glass transition. This is a second order phase transition from the brittle, glassy state into a melted, rubbery state. This is different from melting which is a first order phase transition, and if the material has a melting point, the glass transition temperatur is always at lower temperature than the melting point. 

According to this definition, glasses do not only include your typical window glasses but also most polymers or supercooled special metallic alloys into so-called metallic glasses.

Not all amorphous solids, however, have a glass transition and are therefore not glasses according to the definition.