The basic structure
Amino acids share a common backbone: an amino group at one end, a carboxyl group at the other, and a side chain that distinguishes one from another. When the carboxyl group of one reacts with the amino group of the next, water is released and a peptide bond forms. Repeat that and you have a chain.
The order of the side chains along that chain is the sequence, and the sequence determines almost everything about the resulting molecule: its charge, its solubility, its shape and what it binds to.
Where peptides end and proteins begin
The distinction is conventional rather than absolute. Chains of up to roughly fifty residues are usually called peptides; longer chains, particularly those that fold into stable three-dimensional structures, are called proteins. Nothing changes chemically at the boundary.
The practical difference is how they are made and handled. Short peptides are typically assembled by chemical synthesis; proteins are usually produced biologically. Proteins are also more fragile in handling, because they depend on a folded structure that agitation or heat can disrupt.
Why the distinction matters here
A 15-residue peptide and a 191-residue protein in the same catalogue are not the same kind of material. They are made differently, analysed differently and degrade differently, even though both may arrive as a white powder in a similar vial.
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