Yeah, this is pretty much the case.

The quant derivatives pricing teams at banks are where the stochastic calculus folk tend to head to. Their teams are generally highly respected in this area. Also, banks are doing a different job to funds. Banks are generally interested in assessing the risk or trading risk of these products, either on prop (i.e. with their own funds) or to clients.

Funds tend to concentrate more on statistical/machine learning/econometrics research approaches. The culture is generally more like a research institute thank a bank. They tend to hire more PhDs from Comp Sci, whereas banks will hire directly after MFE or straight out of undergrad.