Navy has never been a boots on ground force like the army. Thus nimitz had only oceanic power. Although whether it was Europe or pacific theatre it was a combined effort. Forgot about wainwright. Patton and other European generals had had massive loss also with little improvement.
The JCS designated Nimitz as Commander in Chief over all Allied forces in the entire Pacific Ocean Area, essentially overseeing the whole Pacific war against Japan as the Commander in Chief, Pacific Fleet and Commander in Chief, Pacific Ocean Areas.
While Nimitz had more control over the sea operations across the Pacific, MacArthur led land-based campaigns in a "specific geographic area" = the "Southwest Pacific Area," which primarily included Australia, New Guinea, and the Philippines. As "Commander in Chief, SW Pacific theater," MacArthur focusing on campaigns in the Philippines, New Guinea, and the Dutch East Indies.
A potion of the USN resources were given over to McArthur to support his follow-on campaigns up thru the Solomon Island Region then on to New Guinea in prep for going to the Philippines.
BTW, the USN had its "boots on the ground" in the form of the USMC which we all know is directly tied to the USN.
Guadalcanal was a combined effort with the USN expending ALOT of resources to stem the Japanese with McArthur calling the ground/air effort there & with the follow-on march up towards Rabaul, which was bypassed.
Afterwards, McArthur was never involved in the central Pacific Island campaigns, Guam and the Marianas.
They two shared the campaign for the Philippines with McArthur with his Army/USN forces and Nimitz with the large fleet forces, and once the Japanese naval forces were defeated Nimitz moved on to focus on Iwo Jima then Okinawa.
Regarding the ETO/MTO the USN had a much smaller role aside from the notable convoy escort work by the lesser forces, and the landing support in the Med and D-Day landings, with the majority of its forces being sent to the Pacific.