Moist air from the Pacific is immediately pushed up by the Rockies and rains out. Almost the entire US West is in the rain shadow, and very dry. Weather patterns pushing north from the Gulf of Mexico and passing over the Great Lakes restore normal rainfall roughly between the Mississippi River and the Appalachians. Since those are very old and weathered mountains, there is a very slight rain shadow to their east, and proximity to the coast evens it out shortly thereafter. Most of the deserts in the US Southwest only get rain from the monsoon thunderstorms from Gulf of California and Gulf of Mexico, because otherwise they're "behind" the mountains all the time.

Obviously, the oceans themselves don't have mountains that cast rain shadows. But they have warm and cold currents. Cold currents have a sort of shadow, because they evaporate less moisture into passing air masses. The warm/cold current split is why San Diego is dry while San Francisco is wet.

Scotland's winds blow over the Norwegian branch of the North Atlantic warm current, rain out over the highlands, and rain out a tiny bit less on the lowlands. The patterns are entirely predictable from orography and oceanic currents. All of Britain is warmer and wetter from the current, and Scotland is where all the mountains are.

Both effects come together at the Atacama Desert, because it's in the orographic rain shadow from the Andes and has a dry coast from a cold ocean current.

Even if the entire planet was covered in ocean, there would still be uneven rainfall patterns, as the circulation currents would be influenced by underwater ridges and seamounts, wind patterns, and seasons.