【Feed】 ,  【nourish】 ,  【pasture】 ,  【graze】  are comparable when they mean to provide the food that one needs or desires.

【Feed】 is the comprehensive term applicable not only to persons and animals but also to plants and, by extension, to whatever consumes something or requires something external for its sustenance. In American but not in British use  【feed】 sometimes takes for its object the thing that is fed.

【Nourish】  implies feeding with food that is essential to growth, health, well-being, or continuing existence.  【Nourish】 more often takes as its subject the thing that serves as a sustaining or a building-up food than the person who provides such food.

【Pasture】 is applied chiefly to animals and especially to domestic animals (as cattle, sheep, or horses) fed on grass.

【Graze】  is often preferred specifically to  【pasture】 when the emphasis is on the use of growing herbage for food.