What tasks you train with one set of features and predict with another?
If you mean completely new set of features for prediction: it will not be helpful. Your model 'learns' something on the training feature space and you hope to apply the learning to new data-points in the same feature space. If the feature space for prediction is completely new, the learning will be useless!
If you mean somewhat new set of features: that often happens in text applications where new tokens might show up in the data which were never seen in training data. Generally handled by some strategy like zero vector or random vector.
Same features but different distribution: this can happen in practice but model performance will go down.