The prohibition of meat and milk is a chok, a commandment whose reason is not readily apparent. Chazal[1] taught that “kid” and “mother’s milk” are just examples of meat and milk. However, there are laws derived from the choice of these words that show that your question has much merit.
R. Akiva derives from the three-fold repetition in the Torah of “a kid” that fowl and certain other animals are excluded from the prohibition. R. Yossi HaGelili says that the law applies to any mammal that requires shechita.[2] He agrees that species that have no mother’s milk (like chicken) are excluded.[3] R. Akiva and R. Yossi HaGelili also argue whether there is a rabbinic prohibition on fowl and milk.[4] The halacha follows the opinion of R. Akiva that there is rabbinic prohibition to eat fowl and milk.[5] The reason for the rabbinic prohibition is that if people become accustomed to eating the meat of chicken in milk, they may forget the aforementioned distinction and eat beef cooked in milk.
Some of the regular restrictions that apply to meat and milk apply to fowl as well. One may not eat fowl and milk together even if they were not cooked together, may not have milk on the table when he is eating fowl (unless he uses a halachic reminder),[6] and must wait up to six hours between eating fowl and dairy.[7]
There are, however, some differences. From the three-fold repetition in the Torah of the above passage we learn that the prohibition includes not only eating meat and milk that were cooked together but also the act of cooking itself and deriving benefit from the cooked mixture. When, however, eating is prohibited only rabbinically, cooking and deriving benefit are permitted.[8] Thus, one could, for example, cook fowl and milk together in order to sell to a non-Jew. (Of course, the pot would then be unfit for cooking food for a Jew.)