The concept of a functional test seems to vary quite a bit more from engineering group to group than your usage indicates.
Sometimes, some unit tests border on functional tests and vice versa, the distinction blurring between two adjacent test cases in a unit test suite.
And sometimes integration suites end up testing single functionalities at a time, depending on the design and/or requirements of the application, and could reasonably be called functional tests.
On my team, I hesitate to emphasize "functional tests" as a standalone group equivalent in semantic distinction to unit and integration tests; the proper scope of a "functional" test is defined, to me, by the way the functionalities of an application were designed and decoupled, which depends on the particular project.
(If your organization uses functional requirements and specifications for software design, it's simpler - a functional test verifies a functional requirement. Unfortunately, having functional requirements as a part of the engineering process is significantly rarer than it should be.)
Sometimes, some unit tests border on functional tests and vice versa, the distinction blurring between two adjacent test cases in a unit test suite.
And sometimes integration suites end up testing single functionalities at a time, depending on the design and/or requirements of the application, and could reasonably be called functional tests.
On my team, I hesitate to emphasize "functional tests" as a standalone group equivalent in semantic distinction to unit and integration tests; the proper scope of a "functional" test is defined, to me, by the way the functionalities of an application were designed and decoupled, which depends on the particular project.
(If your organization uses functional requirements and specifications for software design, it's simpler - a functional test verifies a functional requirement. Unfortunately, having functional requirements as a part of the engineering process is significantly rarer than it should be.)