Connecticut shade is wrapper grown under cloth (or under Ecuador’s persistent cloud) from Connecticut-seed tobacco. The shade keeps the leaf thinner, silkier, and paler than a sun-grown sister plant. The classic American home of that crop is the Connecticut River Valley. A great deal of what is sold as Connecticut wrapper today is grown in Ecuador, where the climate can mimic shade without as much tenting.
The leaf is famous as a mild, even cover — tan to claro — over blends that may or may not be mild themselves. “Connecticut” on a band names the seed and the shade style, not automatically the U.S. state.
It is a wrapper grade. It is not filler slang. When a house says Connecticut, ask whether they mean seed, farm, or color.