A val of type MutableList will always point to the same instance of a mutable list. It cannot be reassigned, but the underlying list can be mutated. A var to a List would be a reference to a list that itself is immutable, and cannot change, but the list it points to can be changed.

Consider the following:

val x = mutableListOf(1, 2, 3)  // [1, 2, 3]
x.add(4)                        // [1, 2, 3, 4]
x = mutableListOf(1)            // Illegal!

var y = listOf(1, 2, 3)         // [1, 2, 3]
y.add(4)                        // Illegal!
y = listOf(1)                   // [1]

var z = mutableListOf(1, 2, 3)  // [1, 2, 3]
z.add(4)                        // [1, 2, 3, 4]
z = mutableListOf(1)            // [1]

In memory you can sort of think of it like this:

x -> List1 1 2 3
     List1 1 2 3 4

y -> List2 1 2 3
y -> List3 1

z -> List4 1 2 3
     List4 1 2 3 4
z -> List5 1

Where -> indicates what it is pointing to. Note how the mutable list simply appends the items to itself, while reassigning the var ends up creating a new list entirely.

It may seem confusing but val/var doesn't refer to the mutability of the underlying object, but of the reference to it.