The words dirigible and airship can be used interchangeably as they mean the same. They refer to any motorized aircraft that rely on a lighter-than-air gas (helium or hydrogen) for lift, thus both blimps and Zeppelins are dirigibles or airships. However, there is a striking difference between Zeppelins and Blimps.
The difference between a Zeppelin and a blimp is that a Zeppelin is a rigid or semi-rigid airship specifically made by the Zeppelin company, while a blimp is a general term for any non-rigid airship. It's important to note that not all rigid airships are Zeppelins, but all Zeppelins are rigid or semi-rigid airships.
Lets take a look at the following drawing of the LZ 130 Graf Zeppelin II rigid airship, which was the successor to the famous Hindenburg Zeppelin airship. Size wise, it was identical to the Hindenburg, having a length of 245 meters. You can clearly see the rigid internal frame inside the hull, consisting of metal girders and wire. You can also see the passenger area, the captain's gondola, crew's quarters, and various corridors throughout the length of the ship.
Below is an image of the Hindenburg Zeppelin airship just after landing. This was always a huge task and required lots of ground-crew combined with good weather conditions. The stripes on the hull caused by the rigid frame are clearly visible.
The Goodyear "Spirit of Innovation" is one of the most famous blimps. As you can see, there are no elongated lines on the complete length of the envelope indicating a rigid frame inside. This type is set to retire in 2017.
Their new model is called the Zeppelin NT, as they are produced by the Zeppelin company in Germany. However, it is important to note that Goodyear still prefers to call them blimps, because of the iconic brand and image associated with words "Goodyear Blimp".
I hope you enjoyed this explanation of the differences between various types of airships. Any comments or further questions are kindly appreciated.
Image sources:
LZ 130 Graf Zeppelin II: airships.net
Hindenburg: NBC News
Ballonets explanation: Scielo
Goodyear "Spirit of Innovation": Wikipedia
Goodyear "Wingfoot One": CNN