These provisions only apply to Research Scholar/Professor category.
Applies to the exchange visitor who was in the U.S. in the preceding 12 months as a J-1 student or as a J-2 dependent. They are not eligible to begin a new program in a research scholar/ professor category until 12 months is completed. For example, someone who was in the U.S. as a J-1 student from January 2017 to December 2019, would need to wait till January 2020 before being eligible to return to the U.S. as a J-1 research scholar/ professor.
Applies in situations when someone who came as a Research Scholar/Professor to U.S. would like to return in the same category as Research Scholar/Professor. They would need to wait 24 months before being able to do so. As mentioned above these 12/24 months bars apply only to Research Scholar/Professor category; the person subject to bar could still return as a J-1 Short-term Scholar or J-1 Specialist or in other visa category such as H-1B, or B-1/B-2.