Is abandoning a pet a crime? The answer depends on how the pet is abandoned and the law of the country, US state, county or city concerned.

Giving up a pet to a rescue organisation for no good reason is abandoning a pet but it is not a crime anywhere in the USA. It is the transfer of ownership of a “chattel”, a household item. Although, arguably it could and should be a crime because the act of abandoning a pet at a shelter often leads to the death of that animal within a short time. I am not sure that everyone who abandons their pet at a shelter realise that they are often killing their cat or dog. Some do and don’t care. They might even desire it. If there is a problem of lack of awareness then an education program should be instigated to make the matter clear.
Chucking a cat through the window of a moving car is both abandoning a pet, being cruel to a pet and causing harm. All US states have comprehensive animal welfare and protection laws outlawing cruelty to animals but the wording does not usually refer to abandonment as a distinct crime.
However, in certain states the act of abandoning a pet is a crime, often a lesser one called a misdemeanor. For instance, in California, “Every person who wilfully abandons any animal is guilty of a misdemeanor”.
Section 597s. (Amended by Stats. 1999, Ch. 303, Sec. 1.) – Cite as: Cal. Penal Code §597s.
(a) Every person who willfully abandons any animal is guilty of a misdemeanor.
(b)This section shall not apply to the release or rehabilitation and release of native California wildlife pursuant to statute or regulations of the California Department of Fish and Game.
And in Florida anyone who “abandons any animal in a street, road, or public place without providing for the care, sustenance, protection, and shelter of such animal is guilty of a misdemeanor.”
828.13. Confinement of animals without sufficient food, water, or exercise; abandonment of animals
(3) Any person who is the owner or possessor, or has charge or custody, of any animal who abandons such animal to suffer injury or malnutrition or abandons any animal in a street, road, or public place without providing for the care, sustenance, protection, and shelter of such animal is guilty of a misdemeanor of the first degree, punishable as provided in s. 775.082 or by a fine of not more than $5,000, or by both imprisonment and a fine.
On the face of it the Florida law is a little softer than that of California but both are in advance of many other states.

Most often pet abandonment is the result of the owner no longer wanting to care for the animal without any good reason (a good reason might be that the person is infirm or too old). This should be a crime as it is in California.
It is difficult, almost impossible on the internet, to find the law of each state, county or city in the USA regarding pet abandonment. I can’t therefore provide a comprehensive breakdown of the law regarding pet abandonment across America but, as mentioned, true cat abandonment will nearly always be accompanied by hardship suffered by the pet or much worse. Therefore the act of abandonment will fall under general animal welfare laws and often be a crime. The final obstacle is that enforcement of the law in this instance is virtually impossible due to a lack of evidence. People intent on abusing animals do it out of sight.
P.S. In the UK the Animal Welfare Act 2006 provides umbrella animal welfare legislation. Pet abandonment would fall within its ambit under section 4 “Unnecessary suffering”.

Oh yeah, forgot to lay out the definition for tamed animal:
‘An animal that is relatively tolerant of human presence.’
All in all, people use the terms domestic and tame; wild and feral interchangeably, ignorant of the nuance of the meanings of the words.
TLDR: ‘Domestication quickly alters the genetics of any species since natural selection is no longer the primary driving force and selective breeding for desirable traits becomes the primary objective.’
It’s simple:
The offspring of the two abandoned dogs are feral while the parents have become strays (definition: a domestic animal with no identifiable owner and found to be wandering). Feral animals are a domestic animal mimicking the behaviors of a wild animal.
You cannot have a wild domestic animal, you have a feral one.
You cannot have a domestic wild animal, you have a tame one.
It takes hundreds of years to turn a species from wild to domesticated.
Wild, native species has nothing to do with animal abandonment and breeding to that location. A wild, native species are not imported or invasion species.
Take the mustang, or if you rather, just the roaming horses in the United States of America. Horses are not native to the USA, so they cannot be a wild, native species. Also, they are not wild, but feral as they were brought over after domestication (small fact: the native horse ancestor in North America went extinct long before settlers arrived). A turkey, however, is a native, wild specie, unlike the pheasant. You can debate whether a certain turkey is feral or wild due to it being a popular farm animal. However, you can certainly tell from the PHYSICAL differences between them which is wild and which is domestic.
Jim, you are here in Florida. I implore you to show yourself and report me as either a hoarder or abuser of cats. I will, happily, give you all info about the rescue group I am associated with.
Just, come out Jim. Stop being a coward.