Hey @Yi_Yao,
The website is showing the conventional unit cell by default for both the lattice parameters and the atomic positions. The problem is that even after selecting “primitive” under lattice, the atomic positions are not updated and keep showing the conventional unit cell. Perhaps this is something that should be fixed by the website admins.
Querying with MPRester() by default returns the primitive cell. Therein lies the difference that you see. If you’re using get_structure_by_material_id() method of MPRester(), you can pass conventional_unit_cell=True and you will see the same structure as you see on the website. If you query using the summary.search() instead, you can do SpaceGroupAnalyzer(struct).get_conventional_standard_structure() to get the conventional unit cell.