That's a good question!

There were organized efforts to exclude non-Japanese from internment as a matter of policy. Americans tried to distinguish between the "good orientals" and the bad ones, although not everyone got the message. The article "How to Tell Japs from the Chinese",” Life Magazine, Dec 22, 1941 link1 link2 is pretty much physiognometric pseudoscience.

The United Korean Committee sent representatives to Washington, D.C. and convinced U.S. officials that Koreans should not be interned with Japanese Americans. The State and Treasury Departments issued a special order stating that Koreans should not be treated as Japanese subjects and enemy aliens but instead should be accorded the same treatment as citizens of allied nations. So Koreans were not interned.

The United Korean Committee issued ID badges with the Korean flag and urged all Koreans to carry these badges as proof that they were not Japanese. Many Koreans also wore buttons saying "I am Korean." This was actually quite common: Many Asian Americans wore buttons or put up signs in their store windows or living room windows saying things like "I am Chinese" or "I am Korean." There are many reports of Koreans and Chinese in the U.S. being harassed and attacked by white Americans who mistook them for Japanese. SOURCE: Ji-Yeon Yuh, 2004.

In a reddit comment 2 years ago, /u/Cordis_melum wrote that "the Chinese Consolidated Benevolent Association printed up insignias, registration certificates, pins and armbands promoting Chinese-American allegiance", and helpfully linked to a photo of pins that advertise the wearer is Chinese.

Howard Yip, a Chinese-American welder from Los Angeles, took to wearing a sign on his back every day to work: "Me CHINESE PLEASE NO JAP. DAMM" SOURCE: USC Jan 1942.

Edit to add: (I can't really speak to the korean-american experience in detail, so you can read this pdf, 24 pages https://evols.library.manoa.hawaii.edu/bitstream/10524/571/1/JL19199.pdf) Chinese Americans had already experienced a boatload of racism and prejudice in the decades before wwII. They were eager to prove they were real Americans, and they worked in factories on the home front, and they fought in the armed forces. But secondly, they had no love for Japan, given that Empire's invasion and terror in East China. Pan-asian-american solidarity wasn't a thing yet. So they played along with the rest of the Americans, denouncing Japanese-Americans for double the satisfaction.

edit: added pdf of Unwanted Allies: Koreans as Enemy Aliens in World War II by Michael E. Macmillan

And one more thing: Japanese-Americans lost jobs and property and businesses when they were rounded up and sent to the internment camps. Chinese-Americans were sometimes complicit in taking over businesses in ethnic neighborhoods, and they also filled agricultural jobs that the Japanese-Americans had worked. But this was due to anti-Japanese sentiment, not acceptance of the Chinese as Americans. Red China and the Cold War ensured that acceptance would take much longer. SOURCE

Not sure what the rules are for adding a secondary question but: I didn't realize the Canadians had internment camps for Japanese, what's the best resource for reading more on that?

Piggyback question, did any Japanese people claim that they were other Asian ethnicities?