The use of human embryonic stem cell cardiomyocytes (hESC-CMs) in tissue transplantation and repair has led to major recent advances in cardiac regenerative medicine. However, to avoid potential arrhythmias, it is critical that hESC-CMs used in replacement therapy be electrophysiologically compatible with the adult atrial, ventricular, and nodal phenotypes. The current method for classifying the electrophysiology of hESC-CMs relies mainly on the shape of the cell's action potential (AP), which each expert subjectively decides if it is nodal-like, atrial-like or ventricular-like. However, the classification is difficult because the shape of the AP of an hESC-CMs may not coincide with that of a mature cell. In this paper, we propose to use a metamorphosis distance for comparing the AP of an hESC-CMs to that of an adult cell model. This involves constructing a family of APs corresponding to different stages of the maturation process, and measuring the amount of deformation between APs. Experiments show that the proposed distance leads to better interpolation and classification results.