The difference is that ‘cognitive bias’ tends to refer to empirically identifiable biases arising from robust studies in the field of psychology, while ‘the unconscious’ is rooted in the older form of psychology known as psychoanalysis, which is often used in a broad and undefined way. This means there is a vast difference in how ‘extensible’ the concepts are. (In general, I don’t trust concepts that are overly extensible, because of the scientific principle that observed relationships don’t necessarily hold outside the range of the data).

For example, we can refer to specific, proven cognitive biases, and you can’t just theorize a new form of cognitive bias without the empirical or clinical evidence. On the other hand, the vague idea of ‘the unconscious’ has been used by various critical theorists to theorize things out of thin air without robust empirical evidence. Like how Marcuse synthesized Freud’s ideas with Marx and Heidegger (who were from completely different fields), and used it to justify his own political work. I don’t think this is logically robust, or even valid, at all.