From a chemical materials standpoint, "plastic" isn't very precise. "Polymer" is preferred. Colloquially and historically we often call them plastics, referring to their general property of plasticity.
To understand polymers, think of a piece of string containing blue-colored beads. If you start with one bead (monomer) and add another (dimer) and another (trimer), and so forth, you can perceive a large difference in the way the string looks with each additional bead you add. But once you get up to, say, 50, adding one additional bead doesn't really mean much. This might be a loose distinction between a polymer and an oligomer. In a polymer, adding or subtracting one or two units just doesn't influence the look and feel of the chain very much. Although, to be sure, the properties DO change, but it takes a larger number of beads to affect an equivalent degree of change once the strand is already large.
There's no real rigorous definition of a macromolecule. IUPAC provides a definition, but it's not really that useful. Virtually everything that would be considered a macromolecule is a polymer of some sort. Proteins are, for example, polymers that have a large variation in the modifications to the primary polymer chain. Likewise, all polymers would be considered macromolecules.