I'm an experimental physicist so please pardon me if my thinking about this is too concrete. Let's say I am taking a measurement over and over and trying to determine the "real" value of something, but my measurement has some inherent noise in it. Let's say I have taken 100 measurements so far.
From what I understand, in Bayesian statistics I would determine the probability that my thing has value X based on the 'priors' - in this case the distribution I have of my measurements so far, and I would update my prediction based on any further measurements I would make with some math.
In frequentist statistics, I would just update my experimentally measured distribution with each new measurement by adding it in to the set of measurements.
How are these two things different? The Bayesian version seems like an unnecessarily cumbersome way to just add a new measurement to my distribution. What am I missing here?