The earth has a complete rock cycle. In weak zones where the continents are moving apart molten rock from inside the earth can burst through as lava to form igneous rock which can build up to form dry land like the Hawaiian islands. Exposed to the elements the rocks can be broken down into small particles forming a rich nutrient soil which can then be washed away by rain as sediment. If that ends up at the bottom of an ocean, the heavy weight of the water above it can compress it into sedimentary rock. Sometimes geological events can occur which raises it back above sea level and the weathering process can begin again. It can also slowly move with the earth's crust to a point where one continent is riding over the edge of another, and then they are sucked down (subducted) into the mantle again, can be melted and reappear later as molten lava which on cooling becomes igneous rock again. However, it can also be compressed and heated not quite to melting and change into metamorphic rock which may be sent back up to the surface by geological upheaval before it has a chance to melt. An example of this is chalk which compresses and changes into the much denser and harder marble. there it once again erodes away and becomes sediment, and so on. So, yes, given time all forms of terrestrial rock are inter-convertible.