Going by the BIP39 standard, it seems that what is stored is the seed (lets call it A). But what is confusing is that people elsewhere seem to be conflating the mnemonic (the 24 or 12 word list, lets call this B) with the seed, while BIP39 appears to say that the seed (A) is derived from the mnemonic (B) by PBKDF2, which is one-way, so they are not the same thing. I always thought the mnemonic is the seed, and the thing that is derived from the mnemonic (seed) is a master private key, and it's the master private key that is stored on the hardware wallet.
In this context, is it correct that
hardware wallets store A?
A is derivable from B, but going the other way is not possible?
can A be called a private key, or is it just some binary value of appropriate length?
I guess one could argue that for some asymmetric key algorithms any value with correct length will do as key, but lets add the condition that it would need to be used for signing or decryption: i.e is A ever used for signing or decryption?