Connecting flights mean that the passenger has to take different flights in the same booking, even if they are operated by different companies. For each flight you will need your own boarding pass and your luggage, depending on the circumstances, might be tagged to your final destination or not.
For flights with a stopover, you will only have one boarding pass with a single origin-destination flight number and, although the plane may make one or more stops at different airports, in most cases you will remain on board or in a designated transit room, if you are required to disembark the aircraft. Your baggage will always travel with you to your final destination.