Flavor-wise, yeah, "divine assassin" is a pretty simple shorthand for an Avenger.
The big difference between Avengers and Paladins can be summed up like this; the Paladin is the Shield of the Faithful, the Avenger is the Wrath of the God. They are holy slayers, killers sanctified in the name of one or more patron gods to strike down foes and cull the ranks of the blasphemers.
In 40K terms... I guess I'd say that Paladins are Space Marines, and Avengers are Assassins.
Mechanically, they're melee-centric Strikers (glass cannon damage dealers) who focus on getting across the battlefield quickly and cutting enemies down with the biggest weapon they can find. Their class feature "Oath of Enmity" basically lets them designate one foe as a heretic and kill them dead quicker by way of being more likely to hit them, so their playstyle revolves around "designate target; pursue target; eliminate target; designate new target".