1. *ASP.NET Core Web API*
It is Specifically designed for building RESTful services.
Functionality: Focuses on providing data through APIs without rendering views. It is Ideal for scenarios where you need to create an API that serves data to various clients (web apps, mobile apps, etc.). If you plan to use a Single Page Application (SPA) framework (such as React, Angular, or Vue), Web API is a great choice. It also Provides mechanisms to secure your API and restrict access based on user identity1.
For example: You can create a Web API to handle requests from both web and mobile clients.

1. *ASP.NET Core Application: It is Used to create web applications that return both views (HTML pages) and data. It Combines server-side rendering of views with data handling and is suitable for traditional web applications that generate HTML pages on the server. If you need to serve both views and data from the same project. It has similar security mechanisms as Web API. For example: A typical MVC application that renders views and handles data requests. **If you need both views and data in a single project, use ASP.NET Core Application and choose ASP.NET Core Web API if you primarily want to build RESTful services and serve data to various clients. If you need both views and data in a single project, opt for ASP.NET Core Application*