Incredible describes the thing — hard to believe, or loosely, amazing. Incredulous describes the person — unwilling or unable to believe. A story is incredible; the listener is incredulous. Only people can be incredulous.
The core difference
The thing and the reaction to it.
- incredible — hard to believe: an incredible claim. Loosely: amazing.
- incredulous — disbelieving: an incredulous stare.
The pattern
This is the same shape as credible/credulous, which is worth learning alongside it. Something credible is believable; someone credulous believes too readily. So: -ible for the thing, -ulous for the person, in both pairs.
The weakened sense
Incredible has drifted to mean simply "excellent" — an incredible meal. That use is standard and unobjectionable, but it has eroded the literal sense, which is one reason writers reach for unbelievable when they mean it precisely.