The basic idea is the same, but be careful of how each verb functions. "Deride" is transitive: you deride something/someone. However, "scoff" is intransitive. You scoff AT something/someone. If you write "you scoff something", the meaning is different: you eat something quickly. Also, "deride" sounds awkward in a colloquial or casual context. It's a formal word.

The word deride means to verbally abuse and downgrade somebody or something, usually laughing. The word scoff means to ridicule, too. You can basically use the terms interchangeably.

Very little in most ways. Deride tends to suggest a more rigorous criticism whereas scoff seems more of an offhand, perhaps not as well thought out, comment.