What is the difference between build.sbt and build.scala?

To give a brief example, this build.sbt:

name := "hello"

version := "1.0"

is a shorthand notation roughly equivalent to this project/Build.scala:

import sbt._
import Keys._

object Build extends Build {
  lazy val root = Project(id = "root", base = file(".")).settings(
    name := "hello",
    version := "1.0"      
  )
}

The .sbt file can also include vals, lazy vals, and defs (but not objects and classes).

See the SBT document called ".scala build definition", particularly the section "Relating build.sbt to Build.scala".

Consider a .scala build definition if you're doing something complicated where you want the full expressiveness of Scala.

Update July 2016 (3 years later)

Build.scala is officially deprecated in sbt 0.13.12

The Build trait is deprecated in favor of the .sbt format

PR 2530 implements that deprecation.
"Appendix: .scala build definition" has been updated.