Cloud Functions is a serverless execution environment for building and connecting cloud services. With Cloud Functions, you write simple, single-purpose functions that are attached to events emitted from your cloud infrastructure and services.
Forms need a server to do much useful, like store the data, send notifications and integrate with other services. You could do those things with a cloud function, but these services help you do as little work as possible.
List of Hosting services that fits in with the serverless world.
A content management system (CMS) is a software application or set of related programs that are used to create and manage digital content.
A static site generator is a compromise between using a hand-coded static site and a full CMS. You generate an HTML-only website using raw data (such as Markdown files) and templates.