Hi @Hemanta,
This is an interesting question! I can understand your confusion.
First, to clarify, these are different polymorphs. To use your Ag2S example, if you download the primitive cell for mp-32868 and the cell for mp-32884 and visually inspect them, you will see they are quite different crystal structures. This is why they have different formation energies, different band gaps, etc.
However, the confusion arises because the CIF file you downloaded reports both primitive cells as having symmetry P1. This is because no symmetry analysis is performed on these structures.
To explain further, there are multiple ways of representing the same crystal structure. You can use a space group (e.g. C2/m) with a basis of atoms, and then under the symmetry operations of that space group you can calculate all equivalent positions of those basis atoms until you have constructed your unit cell. Alternatively, the same crystal can be represented using simply P1 symmetry (i.e. with no additional symmetry operations) and then list every atom in your crystal’s unit cell directly.
When we perform calculations on a crystal structure, we input the crystal using just a list of atoms and the associated unit cell lattice vectors. Notably, the space group is not entered. All our calculation inputs implicitly assume P1 symmetry. It is only later that we perform a symmetry analysis to calculate the space group of our crystal, and that’s what you see reported on the website. Therefore, you can trust the space group displayed on the website to be accurate.
However, for the CIF file you downloaded, we have not performed a symmetry analysis, so the crystal is listed as just P1. Note however that this is simply a lack of analysis: if you plot the atomic positions, you’ll see all the relevant symmetries are still present.
If you would like a CIF file with a symmetry analysis performed (i.e. displaying the correct spacegroup information), just select the ‘Symmetrized’ download option instead.
I hope this helps!
Best,
Matt