If the rocks are igneous then in general:-
Coarse = slowly.
Fine = fast.
However if the rocks are metamorphic or sedimentary then grain size has nothing to do with cooling and indicates other things.
Quartz
Gabbro typically cools slowly beneath the Earth's surface, allowing large mineral crystals to form. This slow cooling process results in a coarse-grained texture in gabbro rocks.
Intrusive rock cools slowly from magma underground, allowing large mineral crystals to form. This slow cooling process is why intrusive rocks, such as granite and diorite, have a coarse-grained texture.
Gabbro cooled slowly underground, resulting in the formation of coarse-grained crystals in the rock. This slow cooling process allows large crystals to grow and develop in the molten rock.
When molten material from inside the Earth cools, it forms igneous rock. The type of igneous rock that forms depends on the rate of cooling and the mineral composition of the molten material. Fast cooling can result in fine-grained rocks like basalt, while slow cooling can create coarse-grained rocks like granite.
Quartz
Extrusive igneous rocks are fine grained due to fast cooling. They cool at a faster rate than most igneous rocks.
Gabbro typically cools slowly beneath the Earth's surface, allowing large mineral crystals to form. This slow cooling process results in a coarse-grained texture in gabbro rocks.
Intrusive rock cools slowly from magma underground, allowing large mineral crystals to form. This slow cooling process is why intrusive rocks, such as granite and diorite, have a coarse-grained texture.
Rocks formed by fast cooling magma are typically fine-grained and include rocks like basalt, andesite, and rhyolite. These rocks cool quickly on or near the Earth's surface, resulting in small mineral grains and a smooth texture.
Gabbro cooled slowly underground, resulting in the formation of coarse-grained crystals in the rock. This slow cooling process allows large crystals to grow and develop in the molten rock.
Generally, large crystals represent slow cooling rates and small crystals represent fast cooling rates. Crystals need time to form and since extrusive rocks cool very quickly, they have very tiny crystals and some don't even have crystals because the rate of cooling was so fast that crystals didn't have time to nucleate. On the other hand, intrusive rocks cool rather slowly allowing crystals to grow.
The difference between an Extrusive and Intrusive igneous rock is the way in which they cool. An Extrusive igneous rock cools very fast on the surface and is created by lava. Since the cooling process is very fast extrusive igneous rocks have very small crystals (fine grained). On the other hand an Intrusive igneous rock cools very slowly beneath the surface and is created by magma. Since the cooling process is very slow intrusive igneous rocks have very large crystals (coarse grained). In some instances there is also a third type of igneous rock. Technically it is an extrusive rock, but it resembles glass. This glass type of igneous rock forms when magma/lava is instantly cooled.
A coarse grained texture, referred to as a phaneritic texture, will be the resultant igneous rock texture. The slower the magma cools the more time minerals have to crystallize and thus grow bigger.
When molten material from inside the Earth cools, it forms igneous rock. The type of igneous rock that forms depends on the rate of cooling and the mineral composition of the molten material. Fast cooling can result in fine-grained rocks like basalt, while slow cooling can create coarse-grained rocks like granite.
The texture is mostly dependent on the amount of time the magma or lava had to crystallize into a solid rock. Volcanic rock is formed from quickly cooling lava (also called extrusive igneous rock), and will have a fine-grained texture. Plutonic rock (also called intrusive igneous rock) is formed from slow cooling magma, and will exhibit visible crystals.
Basalt is fine grained because it is rapidly cooled from molten material. Rapid cooling inhibits the growth of large mineral crystals, as the time that they are allowed to form and grow is lessened.Basalt grains are small because of fast cooling.