Usually older cars start to experience rod knock or piston slap on start up.
Rod knock is when the rod bearings have slight to excessive play and creates a knocking sound which is the rod knocking against the piston or cylinder wall. Excessive play that is not used up under engine load can result in a spun bearing which damages the crankshaft or a thrown rod, which yeah, demolishes the bottom end (usually). I knew a guy that threw a rod through the top of his engine.
Piston slap generally occurs when the bore of the engine is slightly bigger than the piston itself. This usually happens with age as the engine wears. It normally stops after warm-up because the pistons' metal heats up and expands to fill the remaining space in the cylinders.