"Country Sausage" can mean different things to different people but, for me, it conjures up pictures of rustic, basic, solid farm fare.
Folks in general used to live a lot closer to the land than most of us do now. They raised much (or most) of their own food, and their sausage recipes made best use of the bounty that they had closest to hand.
Almost all farm families raised pigs for the larder and much of that pork found its way into sausage.
Not all farm sausage recipes use pork exclusively though. There are many varieties that call for beef, a mixture of beef and pork, or any number of less common sausage meat (including game) in their sausage making.
Country recipes were often for "fresh" sausage, but lots of them also called for curing and and a trip to the sausage smoker.