Spell failure and casting while raging are two different mechanics that both come into play with 'true rages'.
Arcane spells are the only group of spells that is inherently harder to cast in armor. That is, Divine and Druidic spells do not suffer Spell failure from ARMOR or SHIELDS. This is commonly abbreviated to ASF (Arcane Spell Failure).
Casting while raging is a mechanic that almost all spell-casters have to either avoid or work around - most just avoid it, as they can't even get access to true rages without splitting).
A 'true rage' (that is, a Barbarian/Druid/Shifter rage and NOT the Rage spell) has several effects on a character, one of which is the inability to cast spells and use scrolls/wands/clickies. This difference can be important, particularly if you cast Rage and the newbie Sorcerer starts complaining "wHo CaSt RaGe??!!! NoW i CaNt CaSt SpElLs!!" (you 1000% can benefit from the spell 'Rage' and cast any kind of spells you could already cast).
Pre U-51 I hadn't seen any builds outside of a Druid (who uses T4 Natures Protector "Beast Awakened for 23 AP at least) who cast while raging, though with the revamp of Draconic Incarnation, this changed.
At level 20, you can grab "Draconic Rage", which simply says: "You may now cast spells while Raging."
Now while this might not be super effective on a Sorcerer or Wizard, a Druid or even a melee Warlock can use these rages for extra stats including CON, hp, and other attached effects.