Difference between fold and reduce?

In addition to what Lee said, you can define reduce in terms of fold, but not (easily) the other way round:

let reduce f list = 
  match list with
  | head::tail -> List.fold f head tail
  | [] -> failwith "The list was empty!"

The fact that fold takes an explicit initial value for the accumulator also means that the result of the fold function can have a different type than the type of values in the list. For example, you can use accumulator of type string to concatenate all numbers in a list into a textual representation:

[1 .. 10] |> List.fold (fun str n -> str + "," + (string n)) ""

When using reduce, the type of accumulator is the same as the type of values in the list – this means that if you have a list of numbers, the result will have to be a number. To implement the previous sample, you’d have to convert the numbers to string first and then accumulate:

[1 .. 10] |> List.map string
          |> List.reduce (fun s1 s2 -> s1 + "," + s2)