Is this the same as a baking hen?
Probably not. For starters, they're not female and therefore not a hen.
Second, the term "baking hen" is used when referring to a bird only fit to bake. In fact capons are quite moist and tender and will remain so even after they fully mature. This means any capon you get from our farm will be just as good to cook even when they're a year or more old. And because of this capons can be cooked any way you like and should not be limited to just baking which is what you'd choose to do with a bird that's not so moist or tender.
In summary, the term "baking hen" is generally used to describe an older, "past her prime" bird. Most likely an egg layer throughout her life, baking is the preferred method to cook such a bird because it will help tenderize the meat and make them more palpable for the dining room table.