Documentation: "allowed packets not matching the defined policy"

Don't confuse policy with rules.

Manfred: If the POLICY of a chain is, say, DENY, then any packets not matching and rule in that chain will be DENIED. No confusion over that. There is no way for a packet to not match a POLICY; a packet either matches some rule in the chain, or the POLICY serves as the default. It is rules that match, not a policy, the policy being the default for the chain.

It is the language that is the problem here, not a problem in understanding the difference between policy and rules. You seem to mean something I don't understand when the ufw man page uses the phrase "allowed packets not matching the defined policy", which is what I am asking you to explain. Thank you for your patient and thoughtful response.

Where do you see a reference to a "policy in a chain"? I only see one overall default policy (per direction).

See the man pages: http://manpages.ubuntu.com/manpages/eoan/en/man8/ufw.8.html
default allow|deny|reject DIRECTION
              change the default policy for traffic going DIRECTION, where DIRECTION is one of incoming, outgoing or routed. Note that existing rules will have to be migrated manually when changing the default policy. See RULE SYNTAX for more on deny and reject.

I read this the following way:
You first set the overall policy to define what should happen in case that there is no rule for a certain packet, and then you set the rules for those packets that should be handled different than the default policy.
So if the default policy is deny or reject, but a specific rule allows a packet, then this packet is not matching the policy but is still allowed.