Kelvin probe force microscopy (KPFM) is a popular tool for studying properties of semiconductors. However, the interpretation of its results is complicated by the possibility of so-called band bending and the presence of surface charges. In this work, we study two different interpretations for KPFM on semiconductors: the contact potential difference (CPD) interpretation, which interprets the measured potential as the work-function difference between the sample and the probe, and a newer, alternative interpretation proposed by Baumgart, Helm, and Schmidt (BHS). By performing model calculations, we demonstrate that these models generally lead to very different results. Hence it is important to decide which one is correct. We demonstrate that BHS predictions for the Kelvin voltage difference between the p and n parts of a pn junction are inconsistent with a set of experimental results from the literature. In addition, the BHS interpretation predicts an independence from the probe material as well as from surface treatments, which we both find to disagree with experiment. On the other hand, we present a theoretical argument for the validity of the CPD interpretation and we show that the CPD interpretation is able to accommodate all of these experimental results. Thus we posit that the BHS interpretation is generally not suitable for the analysis of KPFM on semiconductors and that the CPD interpretation should be used instead.