Mexico City was "Mexico DF", but was changed years ago to CDMX. That stands for "Ciudad de mexico"

I think there are legal implications. Akin to "Washington District of Columbia"

Decades ago, Mexicans refered to the capital as "el DF" But I dont know about more recently.

Really? Do people call the city just "México", by itself, not "Ciudad de México" or similar?

There is a similar situation in Quebec (the province and its capital city are both just called "Québec" in French, whereas in English we use Quebec/Quebec City). However, there is usually no ambiguity because French grammar requires the definite article for (masculine) names of large territories like countries and provinces, but not for cities. E.g. "Je vais au Québec"[1] = I'm going to Quebec (the province) vs. "Je vais à Québec" = I'm going to Quebec City.

I'm not sure if there is any similar grammatical distinction in Spanish.

1: au is a mandatory contraction for à + le

It could just be people in the area I'm usually in (Yucatan/Q Roo) referring to it that way, but I have heard it from several people.