Got two new cacti, please help me find out what kind they ar

[Theodora]

I bought two new cacti from a local flower shop, but they didn't have a name tag on them, so i have no idea what kind they are. If you could help me identify them i would be eternaly grateful, because i would like to take care of them in the best way that i can. They are like my babies now

[cactushobbyman]

Identification is not my forte but I'll try, Matucana polzii, mammillari polythele inermis. If not, at least someone will correct me.

[CactusMad]

The first one is a gymnocalicium