Polyamides are polymers which contain repeating amide, -CO-NH-, linkages. Proteins are examples of naturally occurring polyamides. The best known manufactured polyamides are often called nylons (the trade name given by the manufacturer, DuPont) and these are aliphatic polyamides.
A peptide bond/link is an amide type of covalent chemical bond linking two consecutive alpha-amino acids from C1 of one alpha-amino acid and N2 of another along a peptide or protein chain. It can also be called an eupeptide bond to separate it from an isopeptide bond, a different type of amide bond between two amino acids.