How can we know if it is a REST Service

In my current project i have been assigned to work on a shared component which should be a web service, which will be consumed by different applications.I can Implement it in REST or SOAP.I choose to build the Service using RESTFull Architecture.I looked in to JERSEY which is a implementation for JAX-RS and SPRING BOOT.My question is declaring a class as @Controller and returning a @ResponseBody for methods makes it a RESTFull service, or we can use @RESTCONTROLLER which ultimately makes that class as a RESTFull service.I have seen the difference and both ways accomplish the same objective.But @Controller and returning a @ResponseBody will it satisfy the advantages of a RESTFULL service like better performance like performance it bears minimal overhead on top of HTTP,Is this a proper REST Service.Like Jersey is there any thing in Spring which implements JAX-RS.I dont want to use Gradle or Maven please suggest me a good jar in Spring which can be used to build a Proper REST Service.

Thanks