The short answer, and why it needs qualifying
In the United States, most research peptides may be lawfully purchased and possessed for laboratory research. They are not controlled substances under the Controlled Substances Act, and they are not scheduled. What they also are not is approved drugs: they have not been evaluated by the FDA for safety or efficacy, and they may not be sold, labelled, marketed or supplied for human or veterinary use.
That distinction is the whole of the legal position. The compound is legal as a research reagent. The same compound becomes an unapproved new drug the moment it is offered or used for consumption. Legality attaches to the purpose and the representation, not to the molecule.