Factory farms, or intensive animal farming as is the technical name, have animals living on a small space that primarily/only eat crops that has been grown elsewhere. In many cases that is the same crops that humans also eat such as soy.
Cattle raised on land that is unsuitable for crop production eat primarily from the land they graze on. Depending on where in the world it is there might be periods like winter where extra "support food" is added, which amount and type depend on weather and circumstance. Support food is usually silage made from hay, grown on land which is deemed too inefficient for other crops. Hay can also be grown on land needing crop rotations, with or without added fertilizers.
Wildlife refuges are sometimes where I live combined with grazing cattle as a cost (and environment) saving method to keep overgrowth down for which otherwise heavy machinery would be needed. It has also been experimented to use sheep for areas with over land power lines, as those otherwise need regular clearing from fossil gulping heavy machinery.
The distinction between factory farming and everything else is sadly lost in most discussions around meat, and when sold it is not marked in the store to distinguish between the two. Most processed food is also said to contain factory farmed meat. Factory farmed meat is basically always a negative for the environment and the animals, but outside of that we got the whole spectrum.