What is difference between REST and API?

REST mostly just refers to using the HTTP protocol the way it was intended. Use the GET HTTP method on a URL to retrieve information, possibly in different formats based on HTTP Accept headers. Use the POST HTTP method to create new items on the server, PUT to edit existing items, DELETE to delete them. Make the API idempotent, i.e. repeating the same query with the same information should yield the same result. Structure your URLs in a hierarchical manner etc.

REST just is a guiding principle how to use URLs and the HTTP protocol to structure an API. It says nothing about return formats, which may just as well be JSON.

That is opposed to, for example, APIs that send binary or XML messages to a designated port, not using differences in HTTP methods or URLs at all.

REST is a type of API. Not all APIs are REST, but all REST services are APIs.

API is a very broad term. Generally it's how one piece of code talks to another. In web development API often refers to the way in which we retrieve information from an online service. The API documentation will give you a list of URLs, query parameters and other information on how to make a request from the API, and inform you what sort of response will be given for each query.

REST is a set of rules/standards/guidelines for how to build a web API. Since there are many ways to do so, having an agreed upon system of structuring an API saves time in making decisions when building one, and saves time in understanding how to use one.

Other popular API paradigms include SOAP and GraphQL.

Note that the above attempts to answer the question in regards to how the terms are commonly used in web development. Roman Vottner has offered a different answer below which offers good insights into the original definition of the term REST with more technical precision than I have provided here.

There is no comparison in REST and API, REST is an API type.

API, in general, is a set of protocols deployed over an application software to communicate with other software components (Like browser interacting with servers) and provide an interface to services which the application software offers to several live consumers.

And Rest is a form of principle which an API follows in which the server provides information whatever the client desires to interact with services.

REST basically is a style of web architecture that governs the behavior of clients and servers. While API is a more general set of protocols and is deployed over the software to help it interact with some other software. REST is only geared towards web applications. And mostly deals with HTTP requests and responses. This makes it practically usable by any programming language and easy to test.