in structural analysis, the classification of structural elements depend on the way that the load transfer, in general basic difference between beam and plate is (one way direction load vs. two way direction) due to the difference in their dimensions. also the plate has a very small transverse dimension compared to its length and width which is not the case in the beam. Based on all above, the behavior will be different between them.
A beam is a long structural member characterized by bending. A plate is thin in one axis relative to other two axis It can use as supports for vertical loads and stiffening other members by connecting them.
The supports and loads are in one line and in the plane for beam and plate respectively.