A direct flight with an interim stop keeps the same flight number for the whole journey.
Connecting flights have two (or more) different flight numbers.
On a connecting flight, the business traveler will have to change planes at an airport en route.
When flight connections are published, there is enough time for the traveler to make the connection and catch the second flight.
It is a good idea to investigate how long the traveler will have to spend at the connecting airport and to check whether there are any executive lounges.
Remember that most business travelers want to spend as little time traveling as possible, so look for the connecting flight with the shortest journey time.