A REST API is an API that meets the requirements for RESTful architecture, which include (among other things):
REST APIs are meant to be more scalable and more lightweight than some other API designs, and RESTful architecture is thus a popular choice for modern API architectures.
A serverless REST API is just a REST API that has been deployed using a serverless architecture. For example, you could build a serverless REST API using AWS Lambda for serverless functions and CockroachDB Serverless as your serverless database.