What is the difference between forward secrecy and key freshness? Is all random private key that generating a unique session key is both forward secrecy and key freshness?
The term ‘perfect forward secrecy’ is bad.  Rather than talking about whether a protocol has perfect forward secrecy, you should talk about when in the protocol you erase keys.  Then, although ‘key freshness’ isn't a common technical term in cryptography, this suggests a clear answer:


Key freshness is presumably about when you generate new keys so that future interactions can't be broken even if the old keys are compromised.
Key erasure is when you erase old keys so that past interactions can't be broken even if your current memory is compromised.