Unbelief = lack of faith, state of not believing in God, religion.

• Living in an age of unbelief.
• He is in the darkness of unbelief.

Unbeliever = Person who doesn’t believe in God, religion, etc.

Disbelief = inability or refusal to accept that something is true or real; scepticism, doubt, amazement, astonishment.

• They stared at the Taj Mahal in disbelief.
• The world reacted with disbelief to the news of his death.
• She shook her head in disbelief.
• Her first reaction to winning the award was disbelief.