Why is chicken white meat, yet duck is red meat?

When it comes to birds with clear white meat/dark meat distinctions, they have one thing in common - they're flightless birds. Chickens and turkeys use their wings for balance, quick escapes and not much more. The legs and thighs are used far more often. This difference in muscular activity means that these muscles have evolved differently. Breasts and wings are dominated by fast-contracting muscle tissue. Thighs and drumsticks are predominately slow-contracting muscles.

In recalling Biology 101, muscles require energy in order to operate. Energy for the fast-contracting muscles comes from glycogen, a carbohydrate in the form of glucose. The slow-contracting muscles fuel comes from fat.
This works differently in birds that can fly. When looking breast meat of ducks or geese, they often has a similar fat content as the legs or thighs.

So in short, dark meat is darker than white because it has more fat. This fat is used to supply energy to muscles that are used on a near continual basis.

Duck and goose are poultry and considered "white" meat. Because they are birds of flight, however, the breast meat is darker than chicken and turkey breast. This is because more oxygen is needed by muscles doing work, and the oxygen is delivered to those muscles by the red cells in the blood. One of the proteins in meat, myoglobin, holds the oxygen in the muscle, and gives the meat a darker color. In other words, chickens and turkeys stand a lot but do little if any flying, so their breast meat is white and leg meat, dark. Game birds spend more time flying so their breast meat may be as dark as leg meat.

https://ask.usda.gov/s/article/Are-duck-and-goose-red-or-white-meat

"Muscles in constant use have red muscle fibre. Red muscle fibre, which looks dark when cooked, has a high myoglobin content."

"Chicken and turkey breasts have white muscle fibre because their chest muscles are adapted for explosive bursts of speed."

"Since Chickens don't fly much the muscles aren't used as often, leaving the meat whiter than birds that do fly - You'll notice that the leg and thigh meat is darker due to more muscle use. Ducks fly more often"