CloudFront Overview:

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So, CloudFront makes your website faster worldwide by caching content at edge locations, while S3 Cross-Region Replication replicates entire buckets for specific regions, useful for dynamic content.

if you use an Amazon S3 bucket configured as a website endpoint, you can’t use the origin access identity feature.

If CloudFront requests an object from your origin, and the origin returns an HTTP 4xx or 5xx status code, there's a problem with communication between CloudFront and your origin.