They aren't at all the same thing, but at a high level they both reduce the amount of fragile/tedious setup-specific futzing you need to do to get a few basic services up.

In 2014, Heroku was the only game in town on the PaaS front. Nobody else was even close.

Java App Servers with their WAR file deployments across a cluster were the closest equivalent.

Docker was the enabler for alternatives.