Spawn is living mushroom mycelium carried on grain, sawdust or another suitable material. It introduces the cultivated fungus into its food. The substrate is that prepared food: straw, wood-based material or selective compost, depending on the mushroom. Casing is a separate surface layer used in crops such as button and milky mushroom. Buying spawn does not mean you have bought a ready-to-fruit bag; ask which stage the supplied material has reached.
Colonisation means the fungus is growing through the substrate. A white surface is only one observation. Compare development across the bag, batch and room, and note any areas that stop advancing. Readings inside growing material and in room air answer different questions because an active crop releases heat. Never interpret a wall thermometer as a direct measurement of the centre of every bag.