The definition of peptide, peptide bond and protein
Two or more amino acids form a peptide. The peptide has the repeated form $\ce{-CO-NH-C(\alpha)R - }$ where R is an amino acid side-chain. The peptide bond is the amide bond N-C. The $\ce{CONH}$ group is planar. A peptide chain can be artificially constructed in the lab from any of the amino acids, its length and composition is then for you to determine. 

A protein is a naturally occurring chain of amino acids folded so as to perform some function. Usually a protein has many amino acids because it has to perform a function in its organism. I'm not sure what the number of amino acids in the smallest protein is, but 20 seems about right. This number is determined by the protein's function, it can be many hundreds. A part of a protein's  backbone is also called a peptide chain.