No, natural weapons are distinct from unarmed attacks.
Usually, an unarmed attack is when a creature attacks without a weapon, using the iterative BAB to determine the number of attacks available (+BAB, +BAB-5, +BAB-10, etc). Unarmed creatures can't use "unarmed attack" for their own attacks of opportunity. Attacking unarmed can provoke attacks of opportunity from the target, and normally cause nonlethal damage.
In some cases, such as natural attacks, an "unarmed" attack does not count as being unarmed:
"Armed" Unarmed Attacks: Sometimes a character’s or creature’s unarmed attack counts as an armed attack. A monk, a character with the Improved Unarmed Strike feat, a spellcaster delivering a touch attack spell, and a creature with natural physical weapons all count as being armed (see natural attacks).
Your bloodrager's claws are natural attacks and don't count as unarmed. Natural weapons are claws, bites, and other pointy bits that are explicitly listed in a creature's stat block or given by some special feature. Natural weapons always threaten spaces within a creature's reach, and can be used for attacks of opportunity. As a full-round attack, a creature can attack with all available natural weapons, instead of using iterative BAB to determine the number of attacks.
Primary attacks are made using the creature’s full base attack bonus and add the creature’s full Strength bonus on damage rolls. Secondary attacks are made using the creature’s base attack bonus –5 and add only 1/2 the creature’s Strength bonus on damage rolls. If a creature has only one natural attack, it is always made using the creature’s full base attack bonus and adds 1-1/2 times the creature’s Strength bonus on damage rolls. This increase does not apply if the creature has multiple attacks but only takes one.
Hypothetically a creature can attack with natural weapons, manufactured weapons, and unarmed attacks altogether, but this involves taking complicated penalties to attack and damage rolls.
For most rule interactions, natural attacks and unarmed strikes are considered separate types of attacks. However there are exceptions. A monk's unarmed strikes benefit from effects that improve natural or manufactured weapons, but not vice versa. The Feral Combat Training feat lets a creature apply unarmed strike feats to a selected natural weapon.