An unbiased estimator is a technical term. It means that its errors in estimation are equally distributed above and below the true value.

Edit to add: I am not sure GP was using the term accurately, either.

An unbiased estimator is one whose expected value equals the true value. Its sampling distribution can be asymmetrical with median not equal to the true value. You seem to be referring to a median-unbiased estimator.

You are correct, of course. It’s too late for me to correct my comment; I slipped up while trying to de-technicalize the definition. Thanks for the correction.

I second this.

An issue I have found with technical minutiae having,for lack of a better term, general names is that they are prone to being used wrong. And once a critical mass of persons start using it wrongly, there's no going back.

> If it's unbiased, that's the same as saying it's random?

No, its deviations from the true value are essentially random.