Mexico is the southern neighbor of the U.S.
It is on southern New Mexico (the US state), but it is located on northern Mexico (the country).
Mexico is the country that borders the southern United States.
Mexico City is the capitol of Mexico, which borders the USA
Both are equally right; however, Southern Mexico is a specific region encompassing three states: Oaxaca, Guerrero and Chiapas; southern Mexico is a more general area that could be anywhere south of Mexico City, down to the border with Guatemala and Belize.
The closest southern neighbor would be Mexico.
The U.S. southern border is formed by Mexico and the Gulf of Mexico.
Warmer, semi-tropical southern climates like Mexico.
Toucans generally like to like in the rainforest. They are native to southern Mexico, and the northern part of South America.
Northern Mexico has a lot more mountains and southern Mexico has a lot more rivers.
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It is the southern border for Texas; conversely, it is the northern border for Mexico.