Insulin is a peptide hormone. It is a small protein made of 51 amino acids in two chains linked by disulfide bonds.

Probably better people to explain it. First sentence on wiki ” Insulin (/ˈɪn.sjʊ.lɪn/ ⓘ;[5][6] from Latin insula 'island') is a peptide hormone produced by beta cells of the pancreatic islets encoded in humans by the insulin (INS) gene.”

Seems like it is very much on the edge of categories thus fits both. And it really is not a giant as proteins go and instead is on smaller end.