API gateway

https only, can provide own certificate
stages from dev, production, etc, similar to tags. They define the path through which the deployment is accessible.
stage can contain variables
multiple versions of the same REST API
no VPC endpoint, but support VPC links
support auth for API methods (AWS signature version 4, lambda authorizers)
gateway can generate API keys and associate them with an usage plan. Call are monitored and included in cloudwatch
throttling/standard rate limit/burst rate limit per second
automatic DDoS protection
gateway can generate client-side SSL certificates to authenticate to backend.

API caching

caching for a stage, gateway caches responses from your endpoint fro a specified TTL in seconds

bills as normal calls

Backends

lambda
AWS step functions
call HTTP endpoint hosted on Beanstalk, EC2, non-AWS hosted
static content (mocks)
Kinesis, some other AWS services