Most of the characteristics of the states of matter can be understood using thermodynamics. Gas can be deformed without volume constraint under pressure. Liquid can be deformed with conservation of volume under pressure. Solid can not be deformed under pressure.
Modern condensed matter theory is concerned with much more states of matter than just the three classical ones. The reason is of course that quantum physics offers much more interaction than classical physics. Interactions between charges and/or spins lead for instance to plasma (metal) or magnetic ordering, and can not be understood without quantum formalism.
Note that the classification between all the states of matter is rather informal, and still under debate, especially for the quantum phases.