I'm pretty new at SML and I would like to make sure I really know the basics. What is the difference between type and datatype in SML, and when to use which?
type declarations just give another name to an existing type. Declaring type t = int * int simply means that you can now write t instead of int * int - it doesn't actually provide any functionality.
datatype definitions let you create brand new types by introducing new data constructors. Data constructors are the keywords and symbols you use to create and pattern-match values, such as the list type's nil and ::. There's nothing particularly special about those identifiers; you can define them yourself as easily as this:
datatype 'a list = nil | :: of 'a * 'a list