While the Triple Helix and Quadruple Helix models are popular in innovation studies, the relations between them have not been addressed extensively in the literature. There are diverse interpretations of helix models in empirical studies that apply them, but these sometimes deviate from the original theses of the models. Such a situation can confuse newcomers to the field in terms of which helix model to apply in their empirical research. We discern that the cause of this research challenge is a lack of systematic comparison of the two models. To bridge the research gap, this paper compares the models from the perspectives of how they were introduced and discussed in the literature and improved and how useful they are in addressing the innovation processes in contemporary society. Our major findings are as follows: First, reviewing the extant literature applying the two helix models for identifying research gaps, we discover that these studies were influenced by three views on the relations between the two models that were located on a continuum between two extreme ends--namely, isolation versus integration of the two models. Second, we provide a systematic comparison of both the advantages and weaknesses of the two models, and this may help researchers choose suitable helix models as conceptual/analytical tools in their empirical innovation studies. Third, our comparison of the two models shows that they are largely supplementary to each other when analysing innovation processes in contemporary society, providing a ground for potential synergy building between the two helix models.