Serverless vs. PaaS vs. FaaS vs. BaaS (Blog.neap.co)

• Platform as a service
• Platform as a Service, allows you to focus on writing code without worrying about the underlying infrastructure. Beyond writing code, the only extra complexity might be around deployment and configuration (e.g., automatic scaling rules, geo-replication).
• Serverless
• Like PaaS, Serverless focuses on writing code without worrying about the underlying infrastructure, but it does it with even more deployment ease and less configuration. 
• Overlaps PaaS and falls into the following two categories
• Function as a service
• Function as a service is a serverless product that hosts a piece of business logic (with usually a small footprint like resizing an image or sending an email). FaaS is well suited to build event-driven architecture. 
• Backend as a service
• Backend as a service is a serverless backend ( e.g. DB hosting) that is a highly available backend that can be set up with barely any configuration and can scale almost infinitely. Once created, the developer focuses on deploying code or data only. 

Evolution of Serverless

On premise

Mix of Cloud and SAAS

Mix of Serverless and SaaS

VM vs. Containers vs. Serverless

The serverless model differs from VMs and containers in that you only pay for the processing time used by each function as it executes. VMs and containers are charged while they're running - even if the applications on them are idle. This architecture doesn't work for every app - but when the app logic can be separated to independent units, you can test them separately, update them separately, and launch them in microseconds, making this approach the fastest option for deployment. (Microsoft).