The terms "hortative" and "hortatory" both describe forms of communication designed to encourage or persuade someone to take action. Both originate from Latin roots that emphasize urging or advising. "Hortative" is derived from the Latin word "hortari," which means "to urge." It is used in contexts where the language or rhetoric is aimed at motivating or stimulating action or behavior through direct encouragement. Similarly, "hortatory," coming from "hortatus," carries a similar meaning, focusing on urging or advising an audience to act in a certain way. In rhetoric, both terms denote speeches or texts that aim to spur the listener or reader to a specific course of action through positive reinforcement or motivational appeal.

On the other hand, "exhortative" and "exhortatory" convey a stronger sense of urging or advising. These terms derive from the Latin "exhortari," meaning "to urge strongly." "Exhortative" describes language or speech that provides strong encouragement or advice, often with a sense of earnestness. It implies a more forceful approach to motivating someone to take a particular action. Similarly, "exhortatory" is used to describe communication that is not only urging but also fervently encouraging action. It carries a connotation of heightened intensity in the attempt to persuade or motivate.

Overall, while all four terms relate to the act of encouraging or urging action, "hortative" and "hortatory" are generally used to describe more moderate forms of encouragement. In contrast, "exhortative" and "exhortatory" are associated with more intense or forceful urging. Each term reflects varying degrees of motivational effort, from gentle encouragement to strong, impassioned urging, highlighting the nuances in how we seek to positively influence others' actions.