Theories of visual confidence have largely been grounded in the gaussian signal detection framework. This framework is so dominant that idiosyncratic consequences from this distributional assumption have remained unappreciated. This article reports systematic comparisons of the gaussian signal detection framework to its logistic counterpart in the measurement of metacognitive accuracy. Because of the difference in their distribution kurtosis, these frameworks are found to provide different perspectives regarding the efficiency of confidence rating relative to objective decision (the logistic model intrinsically gives greater meta-d'/d' ratio than the gaussian model). These frameworks can also provide opposing conclusions regarding the metacognitive inefficiency along the internal evidence continuum (whether meta-d' is larger or smaller for higher levels of confidence). Previous theories developed on these lines of analysis may need to be revisited as the gaussian and logistic metacognitive models received somewhat equivalent support in our quantitative model comparisons. Despite these discrepancies, however, we found that across-condition or across-participant comparisons of metacognitive measures are relatively robust against the distributional assumptions, which provides much assurance to conventional research practice. We hope this article promotes the awareness for the significance of hidden modeling assumptions, contributing to the cumulative development of the relevant field.