Pasture is a more general term meaning "grassland for grazing animals". A meadow is also a field for grazing animals, but it is enclosed by hedges, walls or fences and is usually near the farmhouse. "Meadow" is also the word used for a field where the grass is allowed to grow long so it can be cut to make hay.

Pasture always refers to animals grazing; meadow can be any grassy wild or fairly domesticated place (it has a pleasant connotation); field tends to be agricultural land; grassland could be used for anything worldwide