Accepted answer
96.4 and 99.4 are 3 percentage points apart, which sounds small until you restate it as impurity. VendorInvestigate is leaving 3.6 per cent of the detected area unassigned and Janoshik 0.6 per cent — a factor of 6 between them. The impurity fraction is the quantity that moves when a method changes, and it is the one worth arguing about; the headline is just its complement. Comparable means same column chemistry, same gradient slope, same detection wavelength, same integration convention. Until you have those four from both laboratories, 96.4 and 99.4 are two measurements of slightly different quantities that happen to share a unit.
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.
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.
Buffer versus acid in the mobile phase changes the ionisation state of basic and acidic residues, shifting retention and selectivity — same vial, potentially different separation.
The ICH Q3A impurity thresholds and the relevant pharmacopoeial chapters all specify method validation requirements that almost no research-grade certificate claims to meet.
Compare purity within a single laboratory on the same method, never across laboratories.