Why is a dog that has been saved from the pound called a rescue dog instead of a rescued dog?
A rescue dog is something quite different from a rescued dog.
A rescue dog is a dog that has been placed in a new home after being abused, neglected, or abandoned by its previous owner. The term can also apply to dogs that are found as strays, surrendered by owners for a variety of reasons, including relationship breakdowns, moving home where the owner is unable or unwilling to take their pets, or elderly people who are not permitted to take their dog(s) into a nursing home.
Syntactically, rescue dog is an open-form noun, in the same sense as ice cream.
A dog that has been rescued however, or a rescued dog, is simply a dog that has been rescued from a bad situation. More often than not, a rescued dog is returned to its family.
Syntactically, it is an adjective (rescued) followed by a noun (dog).
Rescue dogs have been rescued from something. But while a rescue dog is also a rescued dog, a rescued dog is not necessarily (and often isn't) a rescue dog.
The Wikipedia article you cite states at the top of it that the article has multiple issues and may need to be deleted.
'Rescue dog' as it stands, is an ambiguous description.
- Chiefly Britain) A homeless, lost or abandoned dog which has been, or will be, re-homed by an animal rescue centre or charity.
- A dog utilised in search and rescue operations; a search-and-rescue dog
A 'rescue dog' may be a dog that has been through (or is still in) a rescue centre. The term 'rescue' (used here as a noun) relates to the title of the establishment which processed the dog, it does not relate - verbally - to the act of rescuing.
When the word 'rescue' is used verbally as a description it relates to the activity of the dog.