There is no relationship. If you are referring to New Moon, the title is so because after Edward leaves Bella she sees a new moon.
werewolves and vampires are born enemies its in there blood to hate vampires
Vampires
There were vampires and werewolves.
Being fictional, they do whatever the author wishes
they are Demetri and Felix.
nothing vampires aren't real
Don't tell the secret. Vampires must be kept secret.Keep control of all the newborn vampires created.Don't create immortal children.
That they change when the moon is full. They are enimies with vampires.
Their name is the Volturi.
The Wolf Pack
In traditional lore, vampires are not specifically affected by the full moon like werewolves are. However, some modern interpretations may include variations of vampire behavior or abilities during a full moon.
Basically you have your vampires vs. werewolves and humans in between. The Cullen's are vampires, the Black's are werewolves and the Swan's are humans.