Boning knives are commonly used specifically for removing bones from meat while fillet knives are commonly used for removing bones and skin from meat, especially fish. There is some overlap as boning knives can be used for filleting and there are some all-purpose, boning/fillet knives.
While some boning knives are flexible, it’s more common for a fillet knife to be flexible. Fillet knives are usually thinner. The flexibility and the thinness help for more precise cutting required for more delicate meats, like fish. Fillet knives are ideal for fish because the thinness and shape of the blade allows for better maneuverability for removing skin. Many fishermen carry a fillet knife amongst their gear to easily gut fish.
Boning knives have a thinner blade than most other kitchen knives but they typically aren’t as thin as fillet knives blades, and are not necessarily flexible. The blades of fillet knives sometimes curve upward while the blades of boning knives are usually straight. This makes boning knives better for larger and tougher meats like pork, beef or chicken, as boning knives are sturdier and thicker than fillet knives.