Previous research on climate-relevant knowledge distinguishes between two types: belief-linked (facts which can be guessed based on general climate beliefs) and belief-neutral (facts which require specific knowledge). To better understand these differences, we used data from nationwide US 2016 and 2021 surveys to develop composite indicators of the two types of knowledge. We analyzed demographic predictors of each type, as well as their effect on climate change belief. Further, we examined the issue of trust in science. The findings point to some novel insights. One, not all knowledge is equal; specific, belief-neutral knowledge in particular is less necessary for climate change belief. And two, trust in science is more relevant for fostering climate change belief than either knowledge type. Although this poses certain challenges, given the ideological divide when it comes to scientific trust, it is also useful information for policymakers and science communicators about where to direct energy and resources when engaging with the public.