spring-boot is a project provided by spring community. It used Java Configuration over XML configuration and provide you default configuration in many scenarios.
For example, previously, you have to manually configure everything. Like DB connection etc.
But in spring-boot, in many scenarios, you just have to give the dependency name and spring-boot will configure it for you.
Spring MVC and Servlets:
Spring MVC internally uses Servlets only, so if you find any other java web project or framework, most probably, that would be using servlets internally.
Now Spring MVC and Spring REST:
First, you need to understand what is REST.
You can implement REST in spring MVC also, but again you have to do so many configurations manually.
Spring REST provides you already configuration, you just have to follow its rules and you could build a FULLY REST API.
REST HATEOS