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master secret key or master private key in functional encryption

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In public-key encryption, we have a pair of private key, public key for each user.
In functional encryption (like Identity-Based Encryption (IBE), Attribute-Based Encryption (ABE) and ...), we have public parameters, master secret key, public key and secret key for each user or functionality.
Asking about terminology,

Why the term "master secret key" was not called "master private key"?
Is there any reason or (subtle) difference between secret key and private key?

Because, the term "secret key" may cause ambiguity with symmetric encryption where we call the shared key, secret key.

I sit in a Tesla and translated this thread with Ai:

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