Resting farm land (fallow) is an old, way old practice, rarely practiced at all today. Modern farmers will use something called a "ley" where they turn crop land into pasture, organic farmers use this especially as part of their rotations. To get a difference in definition:
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Ley:
"a field in which crops are grown in rotation with periods when the field is sown with grass for pasture. Leys are an essential part of organic farming." (Dict. of Agriculture, 3rd ed.) In my understanding a pasture crop for a ley is rarely just something like perennial rye, you will probably see white clover and maybe a forage radish to improve soil structure and fertility.
Fallow:
"a period when land is not being used for growing crops for a period so that nutrients can build up again in the soil or to control weeds - to let land lie" (Dict. of Agriculture, 3rd ed.) Specifically this allowed weeds to grow without being within a crop so they were easily weeded, this in a time before we could deep plough. I remember reading that before there was an understanding of soil structure and nutrients, sometime before the introduction of the four course rotation, that fallowing land was understood to maintain good heart in the soil. Heart being a nonsense word today just meaning stuff grows well.
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Letting land lie fallow works but it has rare use cases today, better to sow a cover crop or control via rotation. Clever rotation should prevent nutrient issues also which is something they didn't understand when using fallows.