Near enough the same thing in everyday use, but the distinction is worth keeping. The heuristic is the shortcut itself, which is often a good one. The bias is the systematic error it produces when memorability and frequency don't line up.
Side by side
Aspect
The heuristic
The bias
Is
A shortcut
Its failure mode
Usually
Works
Misleads
Triggered by
Ease of recall
Vividness ≠ frequency
Verdict
Adaptive
Costly
What each one means
Availability Heuristic
The availability heuristic is judging how likely or common something is by how easily examples come to mind — which makes vivid, recent and heavily reported events feel far more frequent than they are.