Manure is decomposed animal dung. Microbes in the soil release minerals from manure slowly and it helps hold water in the soil.
Compost is rotted plant material. Microbes in the soil release minerals from compost slowly ad it helps hold water in the soil.
Green Manure are plants such as clover or alfalfa. They can be grown in fields and then ploughed into the soil before planting crops.
Artificial Fertilisers are manufactured substances that dissolve easily in water in the soil. They contain the minerals needed in the correct proportions.