Asedimentary rock formed by the compaction and lithification of mud is known as a conglomerate sandstone shale siltsone

The answer is a shale. Shale is a very fine grained rock composed of microscopic particles of clay compacted together. Shale often displays fissility or having many closely spaced bedding planes. Where shale and sandstone occur together, such as in the Gulf Islands of British Columbia, the relatively soft thinly bedded shale forms the bays (recessive weathering) and the points or peninsulas are underlain by resistant hard sandstone. 

Magma is outside the volcano  and lava is inside the volcano.