Thanks buddy!

API Testing is much broader and ensures that services and their dependencies are well-integrated with each other and produce the right result. For example, one service might request data from another one and API testing with Cypress would verify that. Contract testing on the other hand has a smaller scope, I would say on a single team level. If a team wants to avoid setting up the dependencies (services) from other teams and test their stack in isolation then Contract Testing would be preferred. At the end of the day both are necessary, but API Testing (or what you decsribed can also be called a system-test) lives higher on the testing pyramid, while Contract Testing is lower, since it's less constly to write and execute.