A graze is a graze basically. Its where the top layer of skin gets riped off. These hurt as much if not more as its the top layer where the nerve endings are.
A first degree tear is only a short laceration to the perineum and involving the skin.
A second degree tear damages the skin and muscle of the perineum so its much deeper and usually longer. A second degree tear can extend all the way to the anus but not through it or into the sphincter.
A third degree tear involves the skin, muscle of the perineum and the anal sphincter. This is much more nasty and not common. Often a third degree tear is from an episiotomy that has extended through the anus (again uncommon)
A graze can also need suturing although usually not. Some first and even second degree tears don't need suturing although most second degree tears are sutured. It all depends on how the skin comes back together. If its gapping or can only been seen if pulled open and if its bleeding. A tear that sits together normally and doesn't bleed sometimes wont be sutured.