I have spent the last 8+ years in testing talking about Unit testing, System Integration integration testing, User Acceptance Testing, black box, white box, the mythical grey box and many many MORE!
I, like many others, had to go through a round of ISTQB testing exams to ensure I have the right lingo and helped formalise some of the processes such as boundary testing, etc. since moving into the 'Agile' world and experiencing continuous integration (deployment/delivery) practices there is no replacement for experience.
Simplicity is a huge driver for me and I find that testing has been over complicated. In short I see two types of testing and they are functional and non-functional. Everything else is a description of a test phase/phase of product development i.e. Unit testing, Integration, Performance, etc.
I believe we can go one step further as well.
A single test can prove something is functional, if you then multiply a functional test and run it concurrently you have non-functional output. The same could be said for a non-functional test, reducing a load test to a single test and you have a functional test.
You can argue that this is an over simplification and of course there are caveats in this, does it scale?, can the test run concurrently? (should it?), etc.
We should aim for testing simplicity in our delivery and beware individuals that aim to blind you with a list of phases and documents. Simplicity is one of the hardest things to achieve but provides the largest possible gains.