What is the difference between the following words: ḥasanah, thawāb, and ajr?

A good deed is the opposite of a bad deed. Reward (ajr) and recompense (thawāb) are somewhat synonymous, but ajr is more specific than thawāb. Ajr is only given in return for good deeds, while thawāb is given in return for both good deeds and bad deeds.