Vampire: The Masquerade went through Revisions before ending and being replaced by Vampire: The Requiem. In that time, the game acquired a lot of baggage that has since been swept clean. This article summarizes those revisions.
Differences from Vampire: The Masquerade
In many ways, Vampire: The Requiem is very much like its predecessor, The Masquerade, but there are a number of important changes.
The core differences between the games are primarily thematic in nature; in many ways Vampire: The Requiem is closer to Vampire: The Masquerade as it was originally conceived than Vampire: The Masquerade had become over the 13 years since its inception.
The differences can be broadly defined along two lines: physiological alterations designed to make the game more playable, and cultural differences to alter the focus of the game from the action-horror game it had become to the personal-horror game the designers had originally intended.
As far as physiological differences go, the first and most obvious divergence between the games is that the concept of "vampire generation" has been eliminated. A vampire's power is unrelated to that of the vampire who spawned him; instead, he starts off at the lowest level and steadily grows more powerful with age (though he can rise faster by absorbing the power of other vampires).
Vampires now also have a variety of "plot devices" to help them uphold the Masquerade, including a blurred image on video cameras, as well as the previous games' device where a vampire may lick wounds she has inflicted to heal them.
Disciplines have also broadly changed, with a number of subtle alterations in power to make them less helpful in combat, and more helpful in other ways; in addition to this, a number of original clans (some now bloodlines) have changed in theme, and received a change in Disciplines to reflect this (an example might be the Nosferatu, who have gone from being revolting outcasts to actual monsters, with the entirely new Nightmare Discipline to help them maintain this image).
The more obvious and far more far-reaching differences are cultural ones, and this is where old Masquerade gamers will encounter the most fundamental differences.
The first and most noticeable change is in the clans. They have dropped in number from 13 to five, each broadly representing a classic vampiric archetype from literature. This lack of choice in clan has been instituted to force players to think of ways to make their character unique, rather than rely on playing "the last member of a dying race"; a problem which some felt had become endemic among certain players.
The second significant change is the pronounced drop in the importance of a vampire's clan. In Masquerade, your clan informed most aspects of your social interactions with other clan members. In Requiem, the clan one is "born" into is less important than the political faction ("Covenant") one chooses to belong to. (This varies from game to game; sometimes neither has any bearing on the game) This has caused an overwhelming change to the way the politics of the game work; in Masquerade, almost all politics were inter-clan.
The most important change between games, however, is the shift in emphasis on the sect (now called "Covenant") that a vampire belongs to. In Vampire: The Masquerade, a vampire belonged to either the Camarilla (or their argumentative offshoot, the Anarchs), the Sabbat (and their secret, super-violent arm, The Black Hand), the Inconnu, or was isolated and alone. In the story, maybe 50 vampires were Inconnu, and they were all exceptionally ancient and powerful (and rarely, if ever mentioned in supplements after 1st edition; "Lair of the Hidden" being a notable exception). As a result, most vampires were a member of either the Camarilla or the Sabbat. Given that each sect existed in a state of near-perpetual political, ideological, and physical conflict with the other, this made it nigh-on impossible for any real political gaming between the two.
Requiem does away with this perpetual war, to create a world more in keeping with the themes of ennui and politics (and also to yet again scale down the violent action scenes that war made possible). The Covenants are the replacement for sects, and no Covenant is actually at war with any other. Broad comparisons between previous sects and Covenants may be drawn between the Carthians and Anarchs, the Invictus and the Camarilla. In many ways, the Circle of the Crone, Ordo Dracul, and Belial's Brood represent different faces of the Sabbat: the Ordo Dracul being the Sabbat drive to escape the vampiric state, the Circle of the Crone is what has replaced much of the Sabbat's more openly pagan-styled ceremonies and philosophies, and Belial's Brood is essentially how the openly violent and monstrous Sabbat was conceived back in 1st edition Vampire: The Masquerade, before third edition made it more philosophical. Seven is clearly the replacement for The Black Hand, now with significantly less story baggage to it.
A final, and very significant change to the game is the removal of the creation myth involving Caine and the Antediluvians. This story is no longer the only origin story; vampires are uncertain of their origin. Though vampires still conspire against each other, they are no longer puppets of ancient all-fathers, nor do they have a doomsday prophecy looming over them.
In relation to the origin of vampires in the Requiem, White Wolf has this time chosen to leave their beginnings a mystery up to the individual Storyteller to answer--if they choose to answer it all. Due to Torpor, even the oldest Kindred have no clear memory of their past and are forced to guess at their races' beginnings. None of the Covenants even claim to know the origin of vampires, though the Lancea Sanctum and Ordo Dracul do claim that their founders were both uniquely cursed by God directly, instead of being Embraced.
This is partially tied into the addition of the Lancea Sanctum; in original Vampire: The Masquerade, Christianity was assumed to be the "default" truth behind the World of Darkness. The introduction of Kindred of the East and the Laibon in later books caused huge problems for authors to retcon; making the "Caine" origin "true" essentially created huge problems for writers and storytellers who wished to play with a different belief system than Christianity. Thus, the Christian faith has now been utterly externalised, and is represented by its own notably Western Covenant.
Basic Mechanics
Vampires no longer have a Generation. Blood Potency fulfills some of the same functions, but it is a far more variable attribute. Embracing and Ghouling are more expensive in VtR, costing a Willpower point (permanent for embrace, temporary for ghoul) every time the deed is done. This limits Ghoul Abuse and a variety of other tactics used in VtM, especially Mass Embrace.
Clans
There are fewer clans, and all VtR vampires are members of a clan. There are no Caitiff. Bloodlines are now formally defined, with a mechanism for joining them.
Background
Vampires are ahistorical in VtR; unlike VtM with a definite beginning and Vampires who might conceivably remember it, the Torpor mechanism in VtR ensures that the true history of Vampirism is largely unknowable. VtR had a Camarilla, but it ended sometime around the time of Ancient Rome.