Confirmation bias is a cognitive bias where people have a tendency to search out, interpret, or even recall information in a way that reinforces preexisting beliefs. Once a view is formed, people tend to embrace information that confirms that view while ignoring, or even rejecting information that casts doubt upon it. Thus, we don't perceive circumstances objectively. They are always perceived through this filter that favors our currently held beliefs. It is important to note that this effect is stronger for deeply held beliefs and circumstances that elicit a strong emotional response [1].

Motivated reasoning is a cognitive bias which describes our tendency to accept what we want to believe more readily and with less scrutiny than that which we don't want to believe. This is “a form of implicit emotion regulation in which the brain converges on judgments that minimize negative and maximize positive affect states associated with threat to or attainment of motives”[2].

In short, confirmation bias is an implicit tendency to notice information that coincides with our preexisting beliefs and ignore information that doesn't while motivated reasoning is our tendency to readily accept new information that agrees with our worldview and critically analyze that which doesn't. The underlying impetus behind why these biases exist is to minimize cognitive dissonance, which is a result of our innate desire to minimize pain or discomfort (i.e., the pleasure principle [3]). In general, you will find an interplay between all three when people are presented with new information.

1) Let's re-analyze the second example from the post on the availability heuristic as there are more biases worth mentioning in this story: