PUT and PATCH are HTTP methods used to update resources on a server, but they differ in their approach and use cases. PUT replaces the entire resource at a specified URI with the data provided, effectively overwriting the existing entity or creating a new one if it doesn't exist, and is considered idempotent because repeated requests yield the same result. In contrast, PATCH applies partial updates to a resource by sending only the data that needs modification, making it non-idempotent unless specifically designed otherwise, and cannot create new resources if the specified one doesn't exist. Understanding these differences is crucial for developers when designing RESTful APIs or web applications, as it ensures the correct method is chosen for the desired type of update, enhancing both functionality and user experience.