I think you are confused about those.
> Serverless is an Amazon service,
No, it's not.
1. The “Serverless Application Model” is an AWS functionality (a transform for CloudFormation templates for serverless [see #3] compute.)
2. “Serverless Framework” is an open-source product that is independent of Amazon (though it originally targeted only AWS) which supports multiple cloud provider.
3. “serverless” is a broad concept for cloud computing without managing server instances, encompassing, among other things, FaaS—AWS popularized the term, but it's used generally across the industry.
> Firebase is not serverless
Someone tell Google: https://cloud.google.com/blog/products/application-developme...
AWS's "Serverless" (wow that name...) looks like a suite of existing products advertised under one label. From their splash page it looks mostly equivalent to what Firebase, although it seems Amazon has some functionality that Firebase itself doesn't have (necessitating using the full Google Cloud).