Bias: a tendency in judgment
Confirmation bias can make supporting evidence easier to notice and opposing evidence easier to dismiss. The argument someone eventually makes may be valid or invalid, but the search for evidence was already tilted.
Fallacy: a flaw in an argument
A fallacy occurs when the reasons offered do not adequately support the conclusion. An ad hominem attack, for example, substitutes a judgment about the person for an evaluation of the claim.
How they can reinforce each other
A bias can make a fallacious argument feel persuasive, and a fallacy can protect a biased conclusion. Motivated reasoning may encourage someone to accept weak logic from their own side while demanding stronger logic from an opponent.
Which label should you use?
If the issue is selective attention, memory, or judgment, start with bias. If the stated reasons fail to support the conclusion, start with fallacy. In conversation, explaining the missing evidence is usually more useful than winning a dispute over terminology.