Yes to body physiology, but malnourishment in childhood does play a role.
My Korean father-in-law and mother-in-law are well under five feet. My wife is a few inches shorter than my 5'4” height. My youngest niece who lives with us is already almost as tall as me, and will probably be taller when she finishes growing. It appears that Koreans are genetically capable of growing to moderate height; they just haven't had enough food to do so until the current generation. On the other hand, with my Italian genes, being 5'4” makes me about as tall as anyone in my extended family is likely to get.
Back to physiology and body types:
Ask yourself whether a Scandinavian and a Scotsman and a German and a Dutchman and a Frenchman and an Italian and a Greek look physically different, and you'll say, “obviously, yes” (at least on the extremes such as Scandinavian and Greek, less so in between those northern and southern European groups). It's the same way for different Asian ethnic groups. Just as virtually all Americans can tell the difference between most Italians and most Swedes, people familiar with Asians can usually tell the difference between Han Chinese, Korean and Japanese, and all of them look much different than Vietnamese or Laotian or Hmong or the various Indonesian groups. Of course, there's some shading there, especially with the huge size of China and some regionalization in Chinese ethnography over centuries or millenia.
“people familiar with Asians can usually tell the difference”
My Chinese lady friend says I’m very good at that. And the effects of nutrition on height are interesting. A friend and his wife, both from Shanghai, are short, yet both their American-born daughters are over 6 feet! And abdo-lute stunners!