In Greek mythology, the words "Titan" and "God" seem to be used interchangeably. For example, Zeus is a God, but Cronus (his father) was a Titan. So what is the difference between a Titan and a God in Greek mythology?
A 'god' is synonymous to a 'deity'; the Titans and Titanesses were gods, they were members of the second order of divine beings - after Gaia and Uranus, and the other primordial deities.
Cronus and his fellow Titans comprised the second Ancient Greek pantheon (the first comprising of deities such as Ananke, Gaea, and Ouranos), which the younger generation of gods, including Zeus, would later usurp, as the Titans usurped the primordial gods before them. (For more information on this concept of change in dominant deities, read up on the theory of The Golden Age, particularly that of Hesiod, who also wrote the only surviving account of the Titans in his Theogony.)
As for why the Titans have their own order name as opposed to Zeus et al who are simply 'gods', there is debate as to the exact etymology of the word 'titan' but this quote from Hesiod's Theogony states:
"But these sons whom he begot himself great Heaven used to call Titans （Strainers） in reproach, for he said that they strained (τιταίνοντας) and did presumptuous a fearful deed, and that vengeance (τίσιν) for it would come afterwards."
Trans. Evelyn-White, here with side-by-side Greek.
However this is not to say Hesiod was correct; he himself was writing long after the supposed Golden Age ended.
The Greek Gods have their own hierarchy/timeline going on.
First were the primordial deities, the first beings in existence, which included Uranus and Gaia.
Then, descended from the primordial deities were the Titans, which included Chronos and Rhea (Zeus' parents). Note that the Titans were still deities. According to Wikipedia:
Among the first generation of twelve Titans, the females were Mnemosyne, Tethys, Theia, Phoebe, Rhea, and Themis and the males were Oceanus, Hyperion, Coeus, Cronus, Crius, and Iapetus.
The second generation of Titans consisted of Hyperion's children Helios, Selene, and Eos; Coeus' children Lelantos, Leto, and Asteria; Iapetus' sons Atlas, Prometheus, Epimetheus, and Menoetius; Oceanus' daughter Metis; and Crius' sons Astraeus, Pallas, and Perses.
What you call Gods would be the Olympians, who later overthrew the Titans, some of whom were their own parents.
The Twelve Olympians are the major deities of the Greek pantheon, commonly considered to be Zeus, Hera, Poseidon, Demeter, Athena, Apollo, Artemis, Ares, Aphrodite, Hephaestus, Hermes and either Hestia, or Dionysus.
Then, there are a whole host of minor deities, who fall under the "Olympian" umbrella.
There is a family tree denoting the differences between the three classes of deity here.
In short, they are all deities, but different generations of deities.
The word "Titan" is used to denote a class of mythological entities that existed before "Gods" were born and Titans are usually used to describe the creation of the world. All titans were born from Uranus (Sky) and Gaia (Earth), which were the first mythological creatures to be created when the world was formed.
After them, Cronus was born, the cunning, youngest and the most terrifying of his her children (Gaia's) and hated his strong father.
Uranus and Gaia had three sets of children. There were the Hundred-handed ones, or Hekatonchieres, the Cyclopes, and the Titans. Uranus thought the Hundred-handed ones and the Cyclopes were hideous, so he threw them into Tartarus. Gaia did not appreciate this and told Cronus to kill Uranus.
All mythological creatures of that generation are called Titans. Gods are the children of the Titans. Specifically, Zeus was born from Cronus and Rea. Since Cronus feared that some time his childrens would try to seize power, he would eat them, but Rea managed to save Zeus and he tried to seize power when he grew up. The series of events that followed is known as Titanomachy (battle of the Titans), in which the Gods defeated the Titans and became the kings of the world.