Not a whole lot of difference, if you ask me, except for being made from different monomers and being chaotically branched where living matter is more organized.
A few plastics:
Styrofoam: monomer is styrene
Polyethylene: enormous hydrocarbon
Polyvinyl chlorides, though, are different from living matter, in that they bond a chlorine to carbon. That's not typical of life.
A few living things:
Cellulose. Monomer is glucuse.
Fat. Not really a polymer; it's generally a glycerol bonded to three "fatty acids" which are mostly hydrocarbon chain.
Protein. Heteropolymer made from a chain of amino acid residues.
Nucleic acids. Heteropolymer made from a chain of nucleotides.
