Identity and purity are orthogonal, and a high purity says almost nothing about whether the peak is actually what you think it is.
Temperature affects the dynamics of molecular conformation, and if a peptide has proline residues that interconvert on the chromatographic timescale, the peak will split or shoulder at low temperature and collapse at high temperature.
Tailing factor measures peak shape, and a badly tailing peak spreads into the region where small impurities live, forcing tangent-skim integration that assigns tail area to the main peak.
The ICH Q3A impurity thresholds and the relevant pharmacopoeial chapters all specify method validation requirements that almost no research-grade certificate claims to meet.
Worth noting that method standardisation is poor in the research-grade space compared to pharmaceutical work, so identical-looking methods can produce different results.
Compare purity within a single laboratory on the same method, never across laboratories.
edited 17 Nov 2024 by tri_gly_ala — fixed an arithmetic slip in the third paragraph