Layover is a short stop or break on one single journey/itinerary/trip while onto your final destination. Any stop(s) between your ORIGIN CITY and your FINAL DESTINATION CITY (which would be your "journey" or "trip") and is less than 24 hours for international itinerary or less than four hours for domestic itinerary is a layover. You can have more than one layover in a journey or trip. An example is going from New York to Beijing - you depart JFK arrive into LAX in the evening and you catch a flight to PEK the following afternoon.

Stopover is a short visit between your ORIGIN CITY and FINAL DESTINATION CITY and is more than 24 hours. You can have several stopovers in one journey as well. An example would be a "Circle Pacific" ticket where your journey begins in Tokyo and ends in Osaka, but in between you went to Singapore, Hong Kong, Bangkok and Jakarta. The rules are you typically have to complete the journey in one year. You can have multiple stopovers and layovers in a single journey as well.

You can ask to have your luggage picked up at your layover city or transferred to the next flight. For a stopover, you will have to pick up your bag at the next city.