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Both refer to a "republic" in English. The obvious comparison is the names of the PRC and Taiwan, but I'm assuming it's the same word for "republic" in other countries, e.g. how Singapore is known as Sin-ka-pho Kiōng-hô-kok ("Republic of Singapore"), while South Korea (Republic of Korea) is written in hanja as 大韓民國.
Is there a specific definition that defines a nation as a 民國 vis-a-vis a 共和国, or is it just preference at the time of naming?
The term 'Republic' originated from Latin 'res'(entity, concern) and 'publicus'(of the people, public)
'民國' and '共和國' both means 'republic'
'民國' emphasize on the meaning of 'people' (民)
'共和國' emphasize on the meaning of 'public' (共)
China for most of its history, was an empire. All the power belongs to the imperial court. The people(民) had no power at all, therefore 'republic' was translated as '共和國', emphasized on the word '共'(public)- '共和'(public together)- '共和國'(nation of public together)
When Sun Yat Se and his party 國民黨 defeated the Qing Dynasty, ended the imperial rule, they chose to name the new China '中華民國'(Chinese republic/ republic of China) to emphasize China was no longer an 帝國 (empire).
Another reason to choose the name '中華民國' was the word '民' can also represent '民族' as in '中華民族'
Nowadays, most republic in the world are translated as '共和國' in Chinese, because not all republic is made up of mostly one single 民族 like China(中華民族) and Korea (大韓民族).
They are the same thing. 民國 is an older translation of "republic" by Chinese scholars, and 共和國 a newer translation borrowed from Japan-coined Sino-Japanese (discussed below). They could, however, be used quite much interchangeably: the Republic of China Constitution 中華民國憲法 itself says in its first article that "中華民國基於三民主義，為民有民治民享之民主共和國" i.e. 中華民國 is a 共和國.
Nowadays, 共和國 has pretty much superseded 民國 in almost all situations. Only the Republic of China and the Republic of Korea still use 民國 in their names (中華民國 and 大韓民國), but when people describe their form of government, they say they are 共和國.
The only other occasion for which 民國 is used today occurs in reference to the Portuguese Republic in Macao, where "Portuguese Republic" was formerly officially translated as 葡萄牙民國 (now, the official translation is just 葡萄牙共和國). The Avenida da República (Avenue of the Republic) in Macao is translated as 民國大馬路 to day, where 民國 refers to 葡萄牙民國, not 中華民國.
As to whether South Korea call themselves a 民國, the first government-in-exile of Korea, which later became the government of the Republic of Korea, was actually formed in the Republic of China and received assistance from the Chinese government. This is probably pretty much why South Koreans chose the name 民國.
Finally, we'll discuss the Chinese-Japanese origin discrepancy. During the late 19th century, when Chinese scholars and Japanese scholars (all well-educated in Classical Chinese) studied western concepts, they came up with different translations using the same Chinese word-construction principles. However, later on, the translations borrowed Japanese began to dominate even in China. Other examples of such pairs besides 民國 and 共和國 include: "economics" 計學 (Chinese) and 經濟學 (Japanese) and "sociology" 羣學 (Chinese) and 社會學 (Japanese). Now, however, we only use 經濟學 and 社會學 in Chinese.
1.
Republican and imperialism(historical meaning, rule by an emperor), were the two options available to the revolutionaries when KMT founded Republic of China.
Note that republican government is a very broad idea and various groups of people has their own version of understanding. But back at that time those who win over the other side has one in common, that they oppose the ruling by the emperor.
民国 and 帝国 are a pair of notions more understood by Chinese in 20th century when the ROC was founded. That's one reason 民国 is used instead of 共和国. Both Republic of China and Republic of Korea chooses their official translation to be 民国 to differentiate themself from 帝国 such as Qing Empire, Japan Empire or Korean Empire.
2.
Also back to 19-20 century, many east Asian theorists and politicians borrowed the idea of nation 国族 and nation state 民族国家 from their European contemporaries.
On the other side, some people instead support pan-asianism which promotes the unity of all asian people.
Both of them aim to save asian countries from European colonists and preserve independence.
KMT was a nationalist party who want to construct a new national identity and a new nation state. And the south Koreans oppose the pan-asianism as the latter is believed to lead to the invasion by Japan Empire.
For this reason, they want to emphasize that the new countries, ROC and ROK respectively, are nation state owned by their own people.
3.
To sum up, 民国 emphasized two things:
Republican government - as oppose to a government ruled by the emperor
Nation state - as oppose to a country manipulated by foreign nations
中华民国 (Republic of China) founded 1911 to 1949 founded by dr.Sun Yat Sen from 国民党 Party, 中华人民共和国（The People's Republic of China）1949 - present founded by 共产党 Party。
If You want to know the detail you must read china revolution from 1911 to 1949, cause it's rather complicated.
中华人民共和国 and 中华民国, but the difference of the meaning of the phrases 共和国 and 民国.
– user4072
Feb 13 '17 at 12:35
