Peptides are the building blocks of life on earth. Proteins are peptides.
Peptides (and therefore proteins) are made from building blocks called amino acids joined together in strings. In scientific speak, small peptides that contain fewer than 10 amino acids are called oligopeptides, those containing between 10 and 50 amino acids are called polypeptides and those containing more than 50 amino acids are called proteins. In fact, all peptides are called proteins, small proteins or protein fragments in lay English. Often other molecules are bonded to peptides/proteins for example the iron in haemoglobin.
All naturally occurring peptides are coded for by DNA. By analogy with a building, the DNA is the architect's plans and the proteins are the bricks and mortar, but they also fulfill many other functions including cell signalling, self-recognition and much more.
See the article on proteins and the Biological Primer for more information.
Infoplease - Peptide