Difference between Spring MVC and Spring Boot

• Spring MVC is a complete HTTP oriented MVC framework managed by the Spring Framework and based in Servlets. It would be equivalent to JSF in the JavaEE stack. The most popular elements in it are classes annotated with @Controller, where you implement methods you can access using different HTTP requests. It has an equivalent @RestController to implement REST-based APIs.
• Spring boot is a utility for setting up applications quickly, offering an out of the box configuration in order to build Spring-powered applications. As you may know, Spring integrates a wide range of different modules under its umbrella, as spring-core, spring-data, spring-web (which includes Spring MVC, by the way) and so on. With this tool you can tell Spring how many of them to use and you'll get a fast setup for them (you are allowed to change it by yourself later on).

So, Spring MVC is a framework to be used in web applications and Spring Boot is a Spring based production-ready project initializer. You might find useful visiting the Spring MVC tag wiki as well as the Spring Boot tag wiki in SO.

Spring MVC and Spring Boot are well described in other answers, and so without repeating that, let me jump straight to the specifics. Spring Boot and Spring MVC are not comparable or mutually exclusive. If you want to do web application development using Spring, you would use Spring MVC anyway. Your question then becomes whether to use Spring Boot or not.

For developing common Spring applications or starting to learn Spring, I think using Spring Boot would be recommended. It considerably eases the job, is production ready and is rapidly being widely adopted.

I have seen sometimes beginners asking this question because in STS (Spring Tool Suite) there are two wizards: one for creating a Spring Boot project, and another for creating a Spring MVC project. So, my recommendation would be to create a Spring Boot project and choose Web as a module in that.