I'm sure you know the meaning of later... I'll go out later if it stops raining.... He arrived later than expected. The latter is the last of 2 (or possibly more) things mentioned. The purists might say it is the second of 2 things, and is the opposite of former. Some authorities feel that the last of 3 or more things can be called 'the latter.' It can also refer to a group of things: if several groups of things are mentioned 'the latter' would refer to the last group. It also refers to something that is nearer the end than the beginning: the latter part of the year (?October/November/December). And as it means 'near the end/last' it also means 'recent'! We are at the end of many years of history... (albeit an end that moves constantly on!) ... so 'latter-day' means modern/contemporary and latterly means recently. In summary, latter is a word that means 'at the end of something.... time/lists/etc.' And has many uses.

Later is something that will happen at a time subsequent to a reference time. (I will go to the store later.) Latter is referring to the second of two things or persons mentioned (or the last one or ones of several) (Between spinach and ice cream, I prefer the latter.)

Be careful of other spellings: "deference" means submission. You wanted to ask about the "difference" (how two or more things are not the same). "What's the difference between later and latter, in usage?"