Do TPM modules only work for motherboards of the same vendor?

I checked the motherboard user manuals of 4 vendors: Asus, MSI, Gigabyte, Asrock and they are not compatible with each other. As far as I can tell as of 2020 there is no standard TPM header so you must buy TPM from the same vendor as motherboard and even in that case check how many pins you have.

Asus 20-1 (19 pin, old)