Difference between Kubernetes prometheues operator vs helm chart

Both prometheus and the prometheus operator can be installed via helm charts. For installing prometheus operator you have this chart while for deploying just prometheus you have this chart

So your question would rather be: what's the difference between installing an operator vs installing the application directly.

The answer is that the operator does more things for you, one example being that it makes service discovery easier: in order to get data from a service you must usually add an annotation to it, altering the target service, while with the operator you just create a ServiceMonitor resource.