Frequentist statistics is "classical" statistics, the kind most people know. It's often used to control the chance of reporting an effect when there's no real effect (the p-value); in many fields 5% is accepted, which, of course, leaves a lot of false positives among millions of studies.
In the comic, the frequentist is asking: "the machine said yes, what is the probability of that if the Sun hasn't exploded?" Since that probability (the p-value) is less than 0.05, the frequentist concludes the Sun has exploded, which illustrates a common error: mistaking statistical significance for truth.
Bayesians, in contrast, interpret probabilities as beliefs about the world and use experiments to update those beliefs, in accordance with Bayes rule.
In the comic, the Bayesian has presumably started with a strong belief that the Sun has not exploded, and the evidence that the machine says "Yes" one time slightly reduces their certainty but isn't strong enough to convert that belief to "the Sun has (probably) exploded".
Most people (even frequentist statisticians) actually interpret statistics that way, but Bayesian statistics formalizes it mathematically.
The core difference is philosophical, but building on that, Bayesians have built a new set of mathematical tools involving things like conjugate priors, posterior probabilities, credible intervals, and Bayes factors.
The result is a different way of practicing statistics, not merely a difference in interpretation.
In the comic, the frequentist is asking: "the machine said yes, what is the probability of that if the Sun hasn't exploded?" Since that probability (the p-value) is less than 0.05, the frequentist concludes the Sun has exploded, which illustrates a common error: mistaking statistical significance for truth.
Bayesians, in contrast, interpret probabilities as beliefs about the world and use experiments to update those beliefs, in accordance with Bayes rule.
In the comic, the Bayesian has presumably started with a strong belief that the Sun has not exploded, and the evidence that the machine says "Yes" one time slightly reduces their certainty but isn't strong enough to convert that belief to "the Sun has (probably) exploded".
Most people (even frequentist statisticians) actually interpret statistics that way, but Bayesian statistics formalizes it mathematically.