Looks like AWS Faragate pricing is per invocation and duration of tasks.
> Pricing is per second with a 1-minute minimum. Duration is calculated from the time you start to download your container image (docker pull) until the Task terminates, rounded up to the nearest second.
A "task" in ECS means a container. In Fargate, in order to be ready to receive requests 24/7, you have to pay to have a container running 24/7. In that sense, it feels a lot closer to EC2 than it does to Lambda.
> Pricing is per second with a 1-minute minimum. Duration is calculated from the time you start to download your container image (docker pull) until the Task terminates, rounded up to the nearest second.
https://aws.amazon.com/fargate/pricing/