What physical properties differentiates the classes of PT100?
Different (relatively low accuracy) classes of a given construction of Pt100 sensor are similar in construction. The accuracy classes would be determined by accuracy of laser trimming (zero) and the purity and ratios of the materials used (slope). The latter would have to be tested and selected to guarantee the performance. Higher accuracy sensors also tend to be restricted in temperature range (like 0-100°C for 1/10 DIN). 

However, the highest grade sensors use a radically different construction than cheap thin-film laser-trimmed sensors- actual platinum wire loose-wound (to avoid physical stress) on ceramic or glass cores. This is necessary (for one reason) to avoid the relatively large hysteresis errors that thin film sensors have. The best sensors I've seen are physically very large (and thus thermally slow, and poorly suited for real-world applications) as well as costing about as much as a small car. 

There's almost surely some proprietary fiddling going on metallurgically to get the thin film sensors to behave as they do, as well as a lot of other process factors. As an analogy, a 1% resistor that's trimmed or selected to 0.01% has a low initial tolerance but load life (change due to hot operation in a humid atmosphere), tempco, stability over time, voltage coefficient and other factors will still be that of a semi-precision resistor. If you need a real 0.01% resistor in any one of those respects you have to pay for a part that's made quite differently internally.