2 Answers
CloudFront and API Gateway serve different core purposes. Yes, API Gateway does use Cloudfront behind the scenes but lots of AWS services use other services behind the scenes.
I suggest you read up on CloudFront and API Gateway seprerately and you’ll uncover the differences. This will also reveal the AWS documentation you’re seeking as well.
I would add to Scott’s answer:
1) from a DDoS (security) perspective, you’re increasing your posture by applying CloudFront in front of API Gateway/ELB.
2) I wouldn’t put API Gateway vs. CloudFront (which one is best), I think you could/should use both because they serve different objectives;
3) CloudFront + Shield -> S3|API Gateway + Cognito -> ELB|ALB -> EC2|Fargate|Lambda is an AWS "reference architecture" that you can easily find on documentation and/or blog posts;