The numbering is misleading
Both descend from alpha-melanocyte-stimulating hormone, the endogenous peptide that drives melanogenesis. Melanotan I — afamelanotide — is a linear analogue with relative selectivity for the melanocortin-1 receptor, the receptor that governs pigment production.
Melanotan II is a cyclic analogue that binds across the melanocortin family: MC1R, MC3R, MC4R and MC5R. It is not a refined version of Melanotan I. It is a broader one, and the breadth is the entire story.
