Boruta algorithm is a feature selection algorithm. Its purpose is to find all relevant features, and it does that by comparing Z score of original features and shuffled features. Shuffling here is similar to the idea in permutation tests.

Z score of a variable in random forest is average loss when values of a feature is shuffled divided by standard deviation. It’s not related to statistical importance, but used in Feature Selection with the Boruta Package of R as it tells about [quote]fluctuations of the mean accuracy loss among trees in the forest[/quote].