Air fresheners are designed to mask odours with long-lasting fragrance. They do this by overwhelming the odour with a strong or concentrated fragrance, so that you can’t smell the unpleasant odour anymore.
Odour neutralisers aim to eliminate the odour altogether, rather than just masking it. They do this in a number of ways. Some contain odour counteracts to quickly eliminate odours (and sometimes bacteria too) while others wrap up malodour molecules to remove the source of the smell. They do this using a molecule called cyclodextrin, which attract the odour molecules in the air and encapsulate them. This reduces their volatility, which in turn reduces the odour.