What “stretch” means
It is mostly pin-and-bushing wear.
Chains do not normally elongate like elastic. Wear at the bearing surfaces increases pitch, which stops the rollers seating cleanly on the teeth. Replacing the chain at a conservative threshold is usually much cheaper than replacing a chain, cassette and chainring together.
Keep a record of mileage, conditions and measurements. A new chain that skips can reveal that the cassette was already worn.