The terms variance and bias evoke the opposite images from what I expect, so I mix them up every time. In my mind, an overfit is excessively opinionated (“biased”) towards the training set. However, this is wrong. The way to remember this is wrong is that there is no analogous rationale for variance: both an overfit model and an underfit model is likely to have high error on unseen data.
In fact, the overfit model will behave very differently between the training data and a holdout set, which arises from the model memorizing the idiosyncracies of the training set. Like a person whose prediction of a close election changes with every poll, such models are likely to miss the big picture. Hence, variance corresponds to overfitting.
Meanwhile, an underfit model’s performance is limited by assumptions that are not supported by the training data. It is indeed excessively opinionated, but those opinions are not informed by data. Hence, like a Fox News host, an underfit model is biased specifically because it has failed to take reality seriously. Bias corresponds to underfitting.