The part that matters: the single most important distinction is between what purity measures — the fraction of detected material that is your target — and what you actually want to know — how much of the material in the vial is your target.
Column pore size affects mass transfer — a 100 Angstrom packing on a 5 kDa peptide restricts diffusion, broadening the peak and potentially hiding small impurities in the shoulders.
Mobile phase additive choice affects ionisation and peak shape — TFA gives sharp peaks but suppresses mass spectrometry signal, formic acid gives worse peaks but preserves signal.
The ICH Q3A impurity thresholds and the relevant pharmacopoeial chapters all specify method validation requirements that almost no research-grade certificate claims to meet.
One qualification: achieving purity above roughly 98 per cent on a 30-residue peptide is fighting the chemistry of synthesis, not the quality of the purification.
The practical summary: ask for the chromatogram and the method, and ignore the headline number until you have both.