I notice a trend here in my language.
For living chicken singular is chicken and plural chickens.
For living fish singular is fish and plural fishes.
Both have a mass noun (I think that's what I'd call it) version used for the eaten variety of each animal.
I think what's happened is that I've ditched the plurals for fish and chicken and replaced them with their mass nouns. I blame it on an urbanised dialect that's never seen a chicken or fish except on a dinner plate, lol.
What you describe is rather typical English usage. Mass nouns (also called uncountable) typically occur when the substance in question is either, A) impractical to count because each individual piece is too small (wheat, sand, salt), B) impossible to count because it is not tied specifically to size/shape/etc. (water, bread, meat), C) a class or group of things whose inventory/type/etc. may vary considerably (furniture, clothing, stuff), or D) a single concept that does not require counting (justice, happiness, audacity). There are exceptions and anomalies, of course, but this is the general rule.
Countable nouns, on the other hand, are obviously, items that are easily countable, and that are not generally divisible without losing the essential qualities of what constitutes an individual of that class. This is why a living chicken, or say, a car, is countable. The essential requirements for something to be considered an individual chicken or car are rather clearly defined, which is why if you cut a living chicken in half, or a car in half, you don't get two chickens or two cars. Neither half has all the requirements necessary to be considered an individual of its respective class.
On the other hand, it is completely impossible to define what an individual of 'meat' is, because the definition of meat is not tied to its size, shape, weight, or anything related to its physical proportions. If you cut a piece of meat in half, each half may just as validly be called meat as it was before it was cut. This is why saying "I have one pork" makes no sense: because there is no such thing as an individual pork.
So if we say "a chicken" or "chickens" it implies an individual (or several individuals), i.e. a living chicken (or dead but intact chicken), while when we say "chicken" (uncountable), it implies difficulty in defining "chicken" in terms of number, thus, chicken meat.
What I have not touched on yet is that uncountable nouns may become countable when either A) a standard portion is generally recognized, e.g. "a coffee" means "a cup of coffee"; the portion "1 cup" is understood implicitly, even though coffee itself is uncountable; sometimes the portions, so to speak, may be extremely large, e.g. in "territorial waters", the portion is "bodies of", B) classes or types, rather than individuals, are being discussed, e.g. "meats" can mean "types of meat", where "types of" is implicitly understood, or C) poetic license!, e.g. "the ship sank beneath the waters".