Both the Hulk and the Thing were created by the same people: writer Stan Lee and artist Jack Kirby. They created them during Marvel's "Silver Age" in the 1960s.
Ben Grimm, The Thing, has an orange rocky body--created by exposure to cosmic radiation--which gives him great strength and endurance. He's a founding member of the Fantastic Four and often fights evil alongside his teammates.
The Hulk was created when Dr. Bruce Banner was exposed to gamma radiation. He periodically morphs into a giant green behemoth, possessing great strength like the Thing and being pretty much invulnerable to boot.
The Thing is trapped forever in his form, while Bruce Banner becomes the Hulk in times of great stress or anger. The Thing, however, still has his human intelligence, while the Hulk is usually little more than a mindless brute.
The pair first met (and fought) in "Fantastic Four" #25, published in 1964. The fight was a draw: though the Hulk had greater strength, the Thing's speed and comparative intelligence allowed him to balance the scales.