What is the general difference between the words 'rest' and 'remainder'?
The word "remainder" can be used as a synonym for "rest" ("We finished the remainder of last night's stew"). However "remainder" also has certain specific meanings, and is more commonly used in those contexts.
Math: the leftover portion following a division operation. 43 divided by 10 equals 4 with a remainder of 3.
Publishing: a book sold at a discount (usually a work that's losing popularity).