Yes, the two are different. Both are classified as airships or lighter-than-air aircraft, and both apply the principle of trapping a gas that is less dense than "regular" air to provide lift. But there are differences.
Hot air balloons are usually non-rigid and open at the bottom, and rise because of the lower density of heated air. When the air in the balloon cools, the balloon loses lift and descends.
A blimp is a non-rigid airship that rises because the sealed chambers of the ship are filled with a gas that is less dense than air, like helium or (almost not at all any more) hydrogen. The gas does not have to be heated in order for the ship to stay afloat. In contrast, a dirigible is a rigid airship similar to a blimp, and it uses a gas like the blimp does to gain the air.