There is no such thing as "a SHA256 private key". SHA256 is not a private key generation algorithm, it is a hashing algorithm. Do not use SHA256 to generate your private keys as it is not secure. The data that you are hashing will most likely not be random enough to be a secure private key.

Private keys are ECDSA private keys, specifically private keys for the secp256k1 curve. They are just 256 bit random integers.

You can use your Bitcoin private keys with anything that uses ECDSA and secp256k1. You won't have the same address and the import formats will be different because there is additional encoding to differentiate so that people don't accidentally use the wrong addresses.