A working definition
A peptide is a chain of amino acids joined by amide linkages, formed when the carboxyl group of one residue condenses with the amino group of the next and a molecule of water is released. That linkage — the peptide bond — has partial double-bond character, which means it is planar and rotationally restricted. Almost everything that makes peptides behave the way they do in the laboratory follows from this single structural fact.
Because rotation is restricted at the bond itself but free at the flanking alpha carbons, a peptide chain occupies a constrained but still enormous conformational space. Short sequences sample many conformations in solution; longer ones begin to adopt stable secondary structures such as helices and sheets.
A research peptide is simply a peptide manufactured, tested and released for laboratory investigation rather than for clinical supply. The molecule is the same class of chemistry; the difference lies entirely in the specification it is made against and the use it may lawfully be sold for.