What is the difference between ordinary steel plate and medium plate

The ordinary steel plate and medium plate are totally different classification methods.

Ordinary steel plate refers to steel grade, that is, carbon steel, such as Q235, S235 and so on grades of steel; it is the classification similar to low alloy high strength steel.
Ordinary steel plate can be medium plate or open flat plate of hot rolling coil.

Medium and heavy plate refers to the thickness type of steel plate, which is about 6 mm or above. Medium and heavy plate are produced by plate rolling mill (most of which has widening rolling). It is the classification similar to hot strip rolling (no widening).

There are many kinds of steel in medium and heavy plate, such as carbon steel plate, low alloy plate, high strength plate, container plate, bridge plate, etc.