So do producer and creator mean the same thing in terms of TV shows and movies?
...but that doesn't mean that the creator cannot be also a producer.
Simply, the "creator" is the person who came up with or developed the idea for the show...nothing else.
They may take no further part other than coming up with the original concept.
"Producer" is an official credit indicating that the person makes a contribution to the actual production of the show.
There are various "levels" of producer some of which are merely acknowledgements (see Stan Lee and the MCU) and others indicate a financial, executive oversight or creative role in the show.
A television producer is a person responsible for a variety of operations on a network show. These tasks are both creative and administrative. In television, a producer is often a writer. In the case of an executive producer in television, it's a "head writer." An "EP" or "showrunner" as they are more commonly called, or some director-producer-writer hybrid would also be accurate. Typically, a TV producer is tasked with concept development, raising funds, commissioning writers, budgeting, guiding crew members, making casting decisions, and evaluating the project’s overall quality.