Difference between functional test and end-to-end test
As I understand it, the biggest difference between the two is that an end-to-end test requires the test to setup the system components as they are in production. Real database, services, queues, etc. The reason for this is to see that your system is wired correctly (database connections, configuration and such).
A functional test can setup the system with in-memory implementations of your application ports, which would make the test run faster and perhaps allow tests to run in parallel (in some cases). The only thing the test cares about is that a feature works as expected. This can reduce the overhead of setting up certain tests, since preparing 3rd party systems with data can be difficult or time consuming.
What we follow is slightly different and of course difference in just how your team treats each of them. for further clarity,
Functional Test : Tests a feature say login, verify from database if login data is correct, verify if intended event received, or send to a message bus or any external activity in a Prod like environment like staging environment. You test a particular functionality in a real environment.
End to End testing : Test complete feature like, login to app, view product on view page, select product, checkout and do payment. This could cover multiple microservices as well, or maybe multiple teams. If this flow breaks, we can pin point which of the functional tests failed.
Integration Test: Test integration between multiple components, from a wide spectrum of multiple classes to multiple system. Like can UI connect to some external login service, can backend connect to database. If a functional test breaks, we can watch which Int Test failed and so on with unit test.
I think the definitions of functional and end to end testing could vary based on the context of your project. I have seen different people use these terms to describe different things. That being said, usually this is what the 2 terms mean-
Functional testing - This refers to testing the functionality of system based on the requirements. This usually focuses on different requirements of the system and ensure it is working properly. For example - Logging into an application - could be one requirement and then a person could test this functionality manually or in an automated way. Similarly, adding a product to the cart could be one functionality, then, able to make a payment to purchase a product could be a functionality.
End to end testing - This refers to testing the system based on end to end user flows, instead of testing the system has separate components like in unit testing or story level testing. For example - Logging into the application, then adding a product to the shopping cart, then going to the check out screen and then placing an order and then logging out of the application could be one user flow.