The vast majority of country names in Chinese do not contain 国 but are rather purely phonetic transcriptions. Only a handful of countries have 国 in the common name.
And the short names of England, France, America, Germany, Korea, Thai, and China itself contain 国. This seems to suggest that there was a naming convention initially being followed.
Better examples than country names for illustrating this difference between Chinese and English include disease names (mentioned above), fish names, bird names, tree names, flower names, mountain names, river names …