What does perfect mean within perfect forward secrecy and why do some cryptographers disagree with the term? In this blog post, Matthew Green says

Forward secrecy (usually misnamed “perfect forward secrecy”)...

The Wikipedia article on forward secrecy (which the same sentence links to in the blog) says

forward secrecy (FS), also known as perfect forward secrecy (PFS)...

which implies that they are the same thing and nullifies Matthew Green's statement.
Apparently Professor Green's statement is simply a personal disagreement with the term perfect
I'd be interested in knowing how forward secrecy is/isn't 'perfect',(why cryptographers disagree with perfect) and why was the term was originally attached to forward secrecy?
Forward secrecy of key-establishment (KE) protocol means, that compromising of long-term keys of parties doesn't affect secrecy of established keys in the past.
Example to clarify what PFS means.
Say parties A and B have private keys $s_B$ and $s_B$.
Today they run KE and establish a key $k_1$.
They use this key during a session, and then destroy this key.
During this session, attacker eavesdropped all the messages and remembers the transcript $T$ of the session. Obviously, $T$ includes messages of KE,
and subsequent &quot;data&quot; messages, encrypted with key $k_1$.
Tomorrow, attacker somehow gets keys $s_A$ and $s_B$, but not $k_1$ (because $k_1$ was destroyed and forgotten by $A$ and $B$).
And here comes PFS property of KE: even having $T$, $s_A$ and $s_B$, attacker is unable to find $k_1$ and decrypt messages hidden in $T$.
Then answering your question, why in PFS word &quot;perfect&quot; is ambiguous.
It's an opinion of M.Green obviously, but I will try to guess what he means.
Actually I feel pretty the same regarding this term. &quot;Perfect&quot; is ambiguous here.
E.g., we don't use &quot;perfectly secure signature scheme&quot;, we just use &quot;secure&quot;.
Moreover, in cryptography word &quot;perfect&quot; appears sometimes in order to describe
that some property (usually some sort of secrecy) is based not on computational assumptions, but it's perfect - i.e., unconditional and doesn't require any assumptions/hypotheses.
Examples:

perfect zero-knowledge vs zero-knowledge (which could be just statistical or computational)
Perfect secrecy of encryption - term introduced by Shannon https://en.wikipedia.org/wiki/One-time_pad#Perfect_secrecy

So, in cryptography &quot;perfect&quot; is usually a synonym to
https://en.wikipedia.org/wiki/Information-theoretic_security.
But for some stupid reason - not in this case (in case of KE).
So, more clear would be to have a term &quot;Forward Secrecy&quot;, and then, additional &quot;Perfect&quot; would mean that it doesn't require any assumptions and it's unconditional.
But for some historic reason, in literature PFS is used for regular forward secrecy.