Does bias in statistics and machine learning mean the same thing? In statistics, people often talk about unbiased estimators. In machine learning, bias variance trade-off is mentioned all the time. 
Does bias in both contexts mean the same thing? 
Does an unbiased estimator have a bias for the data it tries to model?
 A: Yes, they mean the same thing.
This free chapter covers bias and variance of estimators: http://www.deeplearningbook.org/contents/ml.html
Please see section 5.4, which has a good explanation of what they are.
A: No, they don't. But they're similar.
In ML the learning bias is the set of wrong assumptions that a model makes to fit a dataset. That can be thought of as a measure of how well the model fits the training dataset.
On the other hand, the regular statistic bias is mathematically defined as the average of the absolute error of an estimator. If this number is zero the estimator (or model) is unbidden, if it is positive then the estimator is positive biased, which means the on average the estimation (or predictions) will be always higher than the true value.
They're different because a model can have learning bias (it doesn't fit perfectly the data set) but it is unbiased (the average absolute error is equal to zero, or very close to zero).
For a more detailed explanation read this paper: http://www.cems.uwe.ac.uk/~irjohnso/coursenotes/uqc832/tr-bias.pdf
