There are 3 main types of rock, which are igneous, sedimentary and metamorphic
Igneous rocks are crystalline solids which form directly from the cooling of magma (melted rock), this can take place either underground or above ground. It is formed below ground when magma become trapped in small pockets deep below the earth's surface. As the magma slowly cools down it hardens and becomes igneous rock. Another way it is formed is when a volcano erupts and spews the magma up past the earth's surface. When magma is above land it is called lava. When this lava cools, igneous rocks are formed above land.
Sedimentary rock is a type of rock that is formed by sedimentation, Sedimentation is when large rocks are broken down into smaller particles by methods of erosion. The particles are then transported through moving water such as a river and deposited at an oceon or lake (where ever the motion/current of the water halts). If the particles which have been carried down the river are covered in additional particles, the process of 'lithification' takes place, Lithification is the compaction and cementation of particles which form rock. Compaction squeezes out the fluids and the space which exists between the particles and cementation results when the fluids that are squeezed out are replaced by minerals that crystallized from the fluids. When this process has finished, sedimentary rock is formed. this method forms rocks such as sandstone and limestone, which are both sedimentary rocks.
Metamorphic rock is when two of the aforementioned types of rock fuse together. Normally, metamorphic rock is made by sedimentary rock or igneous rock being subjected to intense pressure and heat when in the vicinity of other types of rock. For example, When magma spews out of a volcano and becomes lava, if it connects with a different type of rock on the earth's surface, the amount of heat from the lava will melt the two rocks together, thus forming metamorphic rock. Another way to obtain metamorphic rock is when the pockets of igneous rock cools and becomes solid when deep underground, it can become pressurised by the earth's layers while being subjected to intense heat, this is another way of forming metamorphic rock. Both processes are called Metamorphism, which means 'change form'.
Therefore the difference between igneous rock and metamorphic rock is that igneous rock is basically, cooled down lava/magma. While metamorphic rock is obtained by igneous rock being subjected to hundreds of thousands of tonnes of pressure and intense heat against another rock.