What I meant with the distinction is:
Martial Arts: for example Tai Chi, is spiritualized (great focus on the philosophical aspect)
Self defense (and sports): for example Karate or Judo, is regulated (rules, etc.)
Combat systems: for example Krav Maga, Systema or a couple old forms like Dojo Bujinkan Budo Taijutsu, no regulations and focused on pure effectivity (straight up combat systems, no fancy rules or anything showy, just what works, as fast and as solid as possible)
I know a lot of people like to use the term martial arts because it reminds people of action movies "yo, I do martial arts, bro" and believe everything is said with that, when in fact there are huge differences between most forms, mostly on how they are nowadays intended to be practiced.
That said, I find that most people who claim to do martial arts actually have little actual expertise/skill in actual fighting because they do not deal with aggressive or people and even most self defense practitioners have little actual knowledge on just how ugly a real fight can be. When some drunk or god forbid a drugged up guy goes berserk, nothing else but going for jugular is going to save your ass, which is a mentality that is routinely and systematically avoided in most martial arts and self defense courses.
I have visited exactly one proclaimed self defense course that I found worthwhile and the instructor started the course stating "run the hell away and failing that: kick it in the crotch and when he's down kick once or twice more just to be sure" and then proceeded onto grappling basics on how to effectively dislocate or break arms using basic grabs as leverage. This guy knew what he's teaching!