The difference is big. To snicker = to laugh, but to try and control your laughter so that it is not too loud. For example: "The students in the back of the class were snickering at a funny video." To scoff = to mock or to scorn something (usually an idea). For example: "When I told him my plan to build an apartment under the ocean, he scoffed at my idea."

You're partly right, "snicker" is almost never used in British English ("snigger" is the equivalent in BE but it's becoming less common because it sounds a lot like a major slur - the words are however, unrelated). It's an unpleasant, nasty way of laughing, often at someone else's misfortune and is usually partly suppressed. "Scoff", on the other hand implies something dismissive and is a way of talking and/or laughing in a way that is meant to ridicule and show a lack of respect. There's nothing hidden about it. So if you scoff at someone's idea for instance, you show that person that you think their idea is ridiculous.

Hello! These are very different reactions to something: to "snicker" is to laugh quietly or discreetly - one could even say in a cowardly way. and to "scoff" is to verbally (openly) show disapproval of something or to mock something or someone - sometimes in a belittling sort of way. I hope that helps!