No, duality and symmetry are not the same thing. Although in many contexts "the dual of" is a symmetric relation, this is not invariably the case (e.g. the dual of the dual of a topological vector space need not be the original).
Moreover symmetry is not just about symmetric relations; it has to do mainly with automorphisms of algebraic, geometric or combinatorial structures. Those structure preserving automorphisms (including trivial the identity mapping) form a group, and we'd refer to it as the symmetry group of the structure.
As you note, there are many kinds of symmetry. Some symmetries have order two but many do not. Indeed the group of symmetries may combine elements that have finite order with those having infinite order, elements that have discrete action with some that are continuous mappings. The symmetries of a right circular cylinder, for example, would include discrete actions like reflection in a midplane as well as continuous actions of rotation about the axis.
If you are looking for a fundamental difference, perhaps it should be noted that duality often involves different categories, i.e. the dual may belong to a different category than the original, while symmetry involves not only the same category but actually a mapping of the same object to itself.
From the dictionary:
verb [...]
- cause one to remember or think of.
- bring the memory or thought of someone or something to (a person or their mind).
- call up (stored computer data) for processing or display.
noun
[...]
So "recall" here means the instances when something was recalled (retrieved) from the data.
The negation would be an instance when something relevant existed, but wasn't retrieved. This is like when you have heard someone's name before, but can't recall their name — can't retrieve it from your memory. Maximum recall means there are no false negatives: whenever there exists something relevant that can be recalled (retrieved), it is recalled (retrieved). It is no surprise that the phrase total recall is used in the context of perfect memory.
(I do feel that it may have been better to call the quantity being measured something like "level of recall" or "amount of recall" or "fraction of recall" or something, but I disagree that the usual meaning (the ones you stated) "has nothing to do with the meaning in such a context". It is the same meaning.)
Best Answer
"Dropped" just means deleted. If the numerator is $A+B+C$ and one replaces it with $A+B$, one has dropped the third term from the numerator.