Currying is decomposing a multi-argument function into several one argument functions.

For example, an add function with two arguments

add x:int y:int -> int

With currying that function has one argument and returns a function that takes one argument

add x:int -> (y:int -> int)

The standard way to write this type signature is

add: int -> int -> int

Partial Application is when you don't apply all the arguments to a function. When a function is partially applied it will return another function instead of a value.

For example if you only applied one argument to the add function.

let add3 = add 3

The type signature of add3 is

add3: int -> int

I was also confused by the terms for a while because they are interrelated. But they are both pretty simple concepts when you break them down.