There was no butcher shop and people caught or grew the animals that they killed. You have to remember there was no good method to keep meat fresh, so it was killed and eaten the same day. Types of meat eaten were beef, lamb, goat, chicken, fowl of all sorts, hare, rabbit, deer, eels, boar, pork.
There were butchers in the middle ages. It is a very old profession. Butchers belonged to the Guild of Butchers - many of the Guild records are still available to read. Butchers were well regarded and in some cities powerful members of society.
Butchers who became members of the Guild had to do an apprenticeship and eventually would become Master butchers. The meat was preserved in salt, smoked or pickled so it would keep for more than a day.
They would butcher beef, pork, horse (yes, sorry horse), fowl, lamb, veal, venison, hedgehog.