But "Functions as a Service" doesn't cover what it is, though.
The following AWS services are "serverless" but would not be "function as a service:"
* S3
* API Gateway
* SQS
* SNS
* Cognito
* DynamoDB
* CloudWatch (logs and metrics)
* Step Functions
In all cases, you are not provisioning or managing servers. Scaling is linear and costs are linear based on how much you use them, and typically based on what's actually being used (bytes stored, requests made, etc.) and not per-node. Because they're all hugely multi-tenant, they also cost almost nothing to use at low scale.
"Functions as a service" covers serverless compute, but it doesn't cover the huge architectural difference (from the developer's perspective) between the services above and rolling your own (for example) S3.