Nag is about repeating. Scold is about something that has already gone wrong.
Children often use nag and scold for any kind of telling-off. The difference is in how often, and when.
To nag is to keep asking or complaining, over and over. 'Have you packed your PE kit? Have you packed your PE kit?' is nagging. It is usually about something that has not been done yet, and the annoying part is the repetition.
To scold is to tell someone off, crossly, for something they have already done wrong. When the dog steals a sausage from the barbecue and Dad says sharply, 'Bad dog!', that is a scolding. It can happen once and be over. A good test: nagging needs a stopwatch, scolding needs a crime.
To keep annoying someone by asking or complaining again and again.
Similar: pester, bother, moan
To tell someone off angrily for doing something wrong.
Similar: reprimand, rebuke
In a cloze or closest-meaning question, the clue is often in the rest of the sentence. Words like 'kept', 'again' or 'all week' point to nag; a single wrong deed that has just happened points to scold.
Definitions and example sentences on this page are the ones a child sees inside Wordrealm, taken from our list of over 1,100 words. It is free to browse, with nothing to sign up for.
Plain-English guides to each test, from the councils’ own pages: Kent Test · Medway Test · Bucks Secondary Transfer Test