quote vs ’ in Lisp

There is no difference, they mean the same thing. 'a is just a shorthand for saying (quote a). Sometimes in the notes you may see (quote a) instead a, this could be just up to whatever compiler the professor used to get the results, or they just computed the result manually and didn’t copy/paste into a compiler.

(quote a) is construct built into the language. It will take all of the arguments to it literally and won’t interpret them at all. If a is bound to a variable it doesn’t matter, it will be looked at as the literal symbol a.

'a is what’s called a reader macro. While almost all of Lisp is the same parentheses syntax everywhere, Lisp allows you to define reader macros to modify the way Lisp syntax is read in. You can think of it as a way to extend the parser that Lisp uses to transform to transform source-code into an internal representation. So there’s a reader macro that basically says “when the symbol ' is encountered, take everything that follows it and wrap it in a list with quote as the first symbol”.

Now, this is much more advanced topics in Lisp that are not covered by this class and so you will not be tested on them at all, but for anyone who was curious, here’s what the ' really means.