The phrase "estudiante/alumno regular" indicates a student in good standing, one enrolled in the school with the ability to continue taking classes.
regular in Spanish ~ regular in English
habitual in Spanish ~ habitual in English
Now for the rest:
"Regular" is a broader term with more nuances in meaning than "habitual." "Habitual" is just an adjective; "regular" can be either an adjective or a noun. The same can be said of Spanish. "Regular" does not mean the same thing in Spanish as it does in English, however ... not in every instance anyway.
It is true that the Spanish word “regular” most commonly means “regular” in English – regular as in according to general rules. The Spanish word “regular" can also mean “stable” and to a lesser degree “mediocre,” but far and away, it is most closely tied with “regular,” so this should be an easy word to remember.
I made some charts and added more to this in a separate post. If you’d like to view it, click on the link below:
If you bother to read it, I hope you find it helpful.