Here's the difference between a nonstop and direct flight
If you want to get where you're going as fast as possible, book a nonstop flight.
These flights take off at your departure city and land at your destination without any stops. However, these are usually also the most expensive flights.
Direct flights, despite the name, will also take you from your departure city to your destination, but will make a stop elsewhere in between.
Some people might get off the flight during this stop, others may get on, but a direct flight does not count as a connecting one as it will have you staying put on the plane. Direct flights, unless otherwise specified, will not have you leaving the plane, unless a plane change is required, though this will usually be noted somewhere, so check the fine print. These flights will be cheaper than nonstop flights, though usually still more expensive than connecting ones.
Despite having a stop, direct flights are called "direct" because their flight numbers do not change (even if the plane does). Connecting flights will always have two (or more) different flight numbers. Think of direct flights as buses: they still take you from A to B without huge detours, but will have an extra stop on the way. Occasionally direct flights will even have more than one stop, so always be sure to check before booking a direct flight. These kinds of flights can also be referred to as "through" flights, especially if they involve a plane change.
Another thing to know about direct flights is that frequent flier mileage is often based on the direct flight's numbers, not the specific legs of the flight. In other words, you may not earn the extra miles flown.
Travel search engines rank nonstop flights highest, followed by direct flights over connecting flights, as those are viewed as more convenient for passengers since you don't have to move. Airlines have direct, or through flights, to appear higher up in searches, as the single flight number makes those flights appear to be a direct, or even nonstop, thus competing with better flights.
So next time you're looking to book a flight, make sure to pay attention to the flight details.