A fallacy is flawed reasoning. For instance, if one concludes that a math proof is correct, not on the merits of the steps of the proof, but because a famous mathematician is providing it, the reasoning is clearly flawed by an appeal to authority. Famous mathematicians can and do make mistakes, and the nature of mathematical proof rests in the consistency of the logic from step to step.
A cognitive bias is systematic error-making in thinking. Let's say you are doing research, but after your PhD advisor looks at your sources, it becomes clear that you are drawing from one set of papers that supports your thesis, while there's an entire set of papers that refutes your thesis. It might be that your choice to do so is consistent with the fact that you routinely avoid any positions critical of your position. In some way, you are confirming your belief through a non-conscious selection of avoiding evidence avoiding disconfirmation.
Both bias and fallacies are types of errors, but a bias is a pattern of making a similar error, and fallacies are errors that apply to a given argument. In other words, fallacies are individual, logical errors in reason, whereas cognitive biases are consistent, psychological errors in thinking.
EDIT
To address claims in the comments: Biases might cause fallacies, but the important thing about biases is that they are systematic. Everybody makes mistakes errors in reason, but one who does consistently in the same way is biased, and it's important not to conflate the two. Think about lies, and pathological liars. Some people tell lies from time to time, but those who do so with zest, zeal, and compulsion are fundamentally different. And biases aren't what we want to believe, they are what we tend to believe erroneously. I personally have biases, but in a bid to improve my reason very much work hard because I don't want to believe error-riddled reasoning. Many people are comfortable with their biases, but many people work hard to overcome them precisely because they want to be closer to being free of errors.
Answer from J D on Stack Exchangelogic - Difference between fallacies and biases - Philosophy Stack Exchange
Has the relationship between cognitive biases and logical fallacies been studied?
Guide to Logical Fallacies and Cognitive Bias
Well I'd definitely believe this chart, but the OP is almost certainly an unmarried hussy who eats their own boogers.
More on reddit.comGood books on biases, logical fallacies and cognitive distortions?
Why are fallacies misleading?
What are fallacies of relevance?
What is the difference between the ad hominem fallacy and the genetic fallacy?
Videos
[Edit for the !remindme folks: I more-or-less managed to answer my own question, with some "help" from Garblin. In the process of finding stand-alone studies on fallacies to demonstrate that yes, they CAN be studied scientifically, I came across the critical thinking literature, which overlaps with research on both cognitive biases and logical fallacies. I haven't quite found what I was originally looking for yet, but I'm pretty confident that it's here if it's anywhere, so I'm going to spend some time exploring the web of which critical thinking articles cite and are cited by others.]
I'm familiar with cognitive biases and logical fallacies independently, but I've found surprisingly little that directly connects the two concepts. It seems reasonable at first glance to expect that informal logical fallacies A/B/C are prevalent in society due to cognitive biases X/Y/Z: writers/speakers who have those biases will make accidentally fallacious arguments (and bad actors will make intentionally fallacious ones), and readers/listeners who have those biases will be persuaded by them, reinforcing the cycle. For example:
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The halo/horn effect biases make the ad hominem fallacy effective
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The anchoring bias makes the anecdotal fallacy effective
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The apophenia bias makes the false cause fallacy effective
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The groupthink bias makes the bandwagon/appeal to popularity fallacy effective
The vast majority of sources I've found on biases and fallacies tends to treat them separately though. For example, most of my links above are from two projects by the same organization (The School of Thought) that never draw connections between the two categories, despite presumably being created by the same team.
If I explicitly search for both terms together on Google Scholar or regular Google and weed out the majority of articles that focus on the differences between them, there are a few articles in line with the ideas above, although they're not written by experts in the field and don't cite any literature on the connection between biases and fallacies:
Perception and Persuasion in Legal Argumentation: Using Informal Fallacies and Cognitive Biases to Win the War of Words
To use a simple analogy, informal fallacies and cognitive biases are two sides of the same coin-one side that represents faulty verbal or written reasoning, and one side that represents faulty mental reasoning.
(regarding the tile: ewww)
Logical Fallacy vs Cognitive Bias – What Is The Difference Between Them?
As mentioned earlier, the important difference between biases and fallacies is that biases affect how you interpret and process information, and fallacies relate to how you construct your arguments and communicate your ideas.
This means that they are closely related to each other; a cognitive bias is often the inclination to commit a logical fallacy in an argument.
Has there been any peer-reviewed research connecting cognitive biases and informal logical fallacies (e.g. testing whether people who display high levels of a particular bias in one context will be more likely to make or be persuaded by arguments with a conceptually related fallacy in a different context), or have any educational/pop science sources gone into more depth on the relationship between them?
If nothing else, this seems like teaching them hand-in-hand could be a good framework for promoting introspection and self-improvement by using justified concerns about manipulation as a hook: "Hey, did you know those so-and-sos are tricking you into acting against your best interests using these sneaky tactics, which oh by the way are so effective because of these quirks in how our brains work..."