The US has an official list of enemies and that includes China. I believe the list was introduced under Trump and is determined by the sitting president:
https://www.ecfr.gov/current/title-15/subtitle-A/part-7/subp...
https://www.ecfr.gov/current/title-15/subtitle-A/part-7/subp...
They're listed as adversaries and not enemies because aiding an enemy country suddenly unlocks a litany of other crimes.
Enemy is very specifically defined: https://www.law.cornell.edu/uscode/text/50/2204
Adversary is very specifically defined: https://www.ecfr.gov/current/title-15/subtitle-A/part-7/subp...
Now let's explore the connotation of enemy. Playing Go against you calling you my enemy is outright wrong. However, if you were my enemy, I would not drink tea and have a laugh with you afterwards. I wouldn't even be playing a game of Go against you, but rather trying to do other not so nice things to you.
Such is the nature of connotation. Being erudite helps here ;) .