To efficiently tune configuration for better system performance (e.g., latency), many tuners have leveraged a surrogate model to expedite the process instead of solely relying on the profoundly expensive system measurement. As such, it is naturally believed that we need more accurate models. However, the fact of accuracy can lie-a somewhat surprising finding from prior work-has left us many unanswered questions regarding what role the surrogate model plays in configuration tuning. This paper provides the very first systematic exploration and discussion, together with a resolution proposal, to disclose the many faces of surrogate models for configuration tuning, through the novel perspective of fitness landscape analysis. We present a theory as an alternative to accuracy for assessing the model usefulness in tuning, based on which we conduct an extensive empirical study involving up to 27,000 cases. Drawing on the above, we propose Model4Tune, an automated predictive tool that estimates which model-tuner pairs are the best for an unforeseen system without expensive tuner profiling. Our results suggest that Moldel4Tune, as one of the first of its kind, performs significantly better than random guessing in 79%-82% of the cases. Our results not only shed light on the possible future research directions but also offer a practical resolution that can assist practitioners in evaluating the most useful model for configuration tuning.