Channel Hop: Batman: The Animated Series aired on Fox Kids, then The New Batman Adventures, Superman: The Animated Series, Batman Beyond, The Zeta Project, and Static Shock aired on Kids' WB!, and Justice League and Justice League Unlimited aired on Cartoon Network.
Exiled from Continuity: Paul Dini and Bruce Timm wanted to use the original Supergirl, Kara Zor-El, in Superman: The Animated Series, but were denied by DC Comics due to their mandate at the time that Superman was to remain the only surviving Kryptonian. Eventually, Kara Zor-El became Kara In-Ze, who comes from Argos, a sister planet to Krypton, and whose race are similar to Kryptonians.
Shrug of God: In the New 52 comic verse, universe 12 follows the Batman Beyond time period. The writers more or less claim it is the same verse as the DCAU or at least close enough to it that they don't really contradict each other.