I've been first in the mammal world of livestock, and then for the last 20 years in the chicken world. I struggled with this quite a bit at first, but have come to accept it.
There are two different ways of expressing the "breed-worthiness" of an animal. In mammals (dogs, cats, horses, cattle, sheep, goats, etc) a "purebred" system is used. In poultry, a "Standard bred" system is used. Note that purebred is not capitalized, whereas Standard bred is capitalized.
The term purebred refers to a traceable lineage where there have been no outcrossings with different breeds (or in some rare breeds, there are acceptable limited outcrossings, which is not common). The offspring is considered purebred if both the dam and all possible sires are known purebred. The specific sire does not need to be known for an animal to be purebred (ie, a flock of sheep, all purebreds, with 3 rams kept in a pasture with 100 ewes -- all the possible sires are purebred, but which specific ram sired any particular lamb is impossible to know without genetic testing). If the specific sire is known (either because it is the only possible sire, or through genetic testing), and both the sire and dam are registered, then the offspring can be registered. That is what is required for a mammal to be considered purebred, or to be eligible to be a registered purebred. Absolutely nothing is required other than word of mouth, or if registered a paper trail, both of which can be false. The other hitch in this system -- it doesn't matter is the animal is a good representative of the breed. You can have an animal that looks nothing like the breed standard in any feature and it is still considered purebred, or even a registered purebred, under this system. As an example, puppy mills crank out thousands of registered purebred puppies every day that look nothing like what is proper for that breed, but they are still registered purebreds, and every one of them is sold for hundreds or even thousands of dollars to naive buyers. That's the purebred system.
The Standard bred system used for poultry comes at the problem from the opposite side. Quality is the ONLY thing that matters! There are established "Standards" for different areas in the world. In the US, there is the American Poultry Association (APA) Standard of Perfection (SOP). In the UK, there is the British Poultry Standard (BPS). There are others too, but those are the two that I am most familiar with. Many non-US/non-UK shows use either the SOP or the BPS as their Standard. The SOP and the BPS are not always the same for the same breed, so a breeder has to decide on their breeding goals -- which Standard are you going to breed towards. Usually it's not an issue, but sometimes it is. As an example, I breed Red Dorkings. They are a UK breed. However, the (US) SOP for them is quite different than the (UK) BPS both in terms of size and color, although most other aspects are similar. As a US breeder, if I were to show them, I would have to choose to either use the BSP and lose shows even if I had excellent birds, or to use the SOP to attempt to win. Since I don't show, it's not an issue for me, but it might be for others if they prefer the Standard of the breed's country of origin instead of their local Standard. But I digress. For poultry, as opposed to mammals, pedigree is irrelevant when judging a bird (obviously, it's not irrelevant when breeding a bird, but that's a different subject), and therefore "purebred" isn't an official thing in poultry. If a bird meets the Standard for that breed, then by definition it is that breed. If someone can create a very poor quality black Cochin that looks exactly like a great quality black Croad Langshan, then by definition that bird is a black Croad Langshan, regardless of genetics. (On the other hand, if someone were to breed a Rottweiler that was such poor quality that it looked like a nice Doberman, it would still be a poor quality Rottweiler, not a good quality Doberman.) With mammals a purebred is defined exclusively by genotype regardless of phenotype. With poultry a Standard bred is defined exclusively by phenotype, regardless of genotype. Or to put it in less technical terms -- with mammals, it can be a purebred regardless of what it looks like, and in poultry it's a Standard bred if it looks like a Standard bred, regardless of what its parents were. Totally different systems, each with great benefits and great flaws.
Now obviously, if you're breeding quality stock, you have to take both aspects into account. As a breeder who selects specific animals for breeding, you will be most successful at consistently producing the best offspring if you know the history of the animal's genetics and the history of the animal's phenotype for several generations back. That usually takes excellent records and the judgement that comes with experience. You can't ignore phenotype if you want to breed quality mammals, because not all buyers are naive enough to think that being a purebred, or even a registered purebred, means anything. And you definitely won't win shows with mammals that don't represent the breed well. With poultry, that one fluke black Cochin that won best of breed as a black Croad Langshan might enjoy its ribbon, but it won't have any value beyond that, as it won't breed true. There's too many variables in its genetics, so it's simply a one-and-done kind of bird. It has no value in the breeding pen until its line starts producing chicks that consistently look like Croad Langshans. At that point, you've recreated the Croad Langshan breed, and your birds are now considered Croad Langshans and are no longer Cochins. Just a different version of reality compared to what is done with mammals.
So the question was, how do I use the term "purebred chickens?" I use it as a way to determine a person's experience in the hobby. An experienced person will refer to a line as Standard bred. An inexperienced person will typically refer to a line as purebred. They're trying to mean the same thing, even though it's not the same thing. When someone refers to purebred poultry I know that they're a little earlier in their breeding career, and I give them a little more mentoring (without a condescending attitude -- the goal is to be helpful, not holier-than-thou). There's nothing wrong with being a beginner. People who are asking are trying to do things right, and they deserve the guidance of experienced breeders. Without that, the hobby of poultry keeping will die out, and even more of our beloved Standard bred birds will become extinct.