They're not interchangeable in Swedish. en elev is for younger students who study at grundskolan and gymnasiet whereas en student studies at a college or university. (I don't think they're interchangeable in English either, rather it's that in US English they prefer to call both student?)
Yes, some adjectives are irregular in this way. It's a group of adjectives that in themselves make the noun "definite enough". So we say
samma mål 'the same goal'
nästa vecka 'next week'
förra året 'last year'
sista gången 'the last time'
As you can see, some of these adjectives prefer the noun to be definite, others don't. Regular adjectives would always take the definite form + have the front article: den röda boken 'the red book'.
According to the comments in several of the other exercises, English pupil is only for primary and secondary education (K-12 or equivalent) while student can include those in college. I personally never knew the difference.
In Swedish, elev = pupil but student = student and does not apply to those preuniversity pupils.