Scala's sealed abstract vs abstract class

The difference is that all subclasses of a sealed class (whether it's abstract or not) must be in the same file as the sealed class.

As answered, all directly inheriting subclasses of a sealed class (abstract or not) must be in the same file. A practical consequence of this is that the compiler can warn if the pattern match is incomplete. For instance:

sealed abstract class Tree
case class Node(left: Tree, right: Tree) extends Tree
case class Leaf[T](value: T) extends Tree
case object Empty extends Tree

def dps(t: Tree): Unit = t match {
  case Node(left, right) => dps(left); dps(right)
  case Leaf(x) => println("Leaf "+x)
  // case Empty => println("Empty") // Compiler warns here
}

If the Tree is sealed, then the compiler warns unless that last line is uncommented.