"regime” is typically used to talk about government, usually a highly authoritative one. Example: The regime would hear of no dissant. “regimen” is usually used with talking about scheduled medical treatment. Example: They took a regimen of 1 Advil daily.

The two words are different in modern English (even though they are one word in Latin and other languages). The following definitions are from Google. Note that with both words, the first definition is much more common than the second one (and the less common definition of one word is similar to the much more common usage of the other word): regimen: 1. a prescribed course of medical treatment, way of life, or diet for the promotion or restoration of health. 2. Archaic: a government regime: 1. a government, especially an authoritarian one. 2. a system or planned way of doing things, especially one imposed from above.

Regimen is archaic and has another more common meaning now. Regime is all I recall seeing and hearing in use in the recent past.