Many years later... there's Codeception framework now that you can use to do Unit, Integration and Functional tests.
Codeception uses PHPUnit as a backend for running it's tests. Thus, any PHPUnit test can be added to a Codeception test suite.
In unit tests, you would mock database access, file system, HTTP Requests and other components to isolate code and make it faster.
Integration tests doesn’t require the code to be executed in isolation, that means you will be using those components for real and check the output/results for what was expected.
To ilustrate, take a look at this integration test example from Codeception DOC:
<?php
function testSavingUser()
{
$user = new User();
$user->setName('Miles');
$user->setSurname('Davis');
$user->save();
$this->assertEquals('Miles Davis', $user->getFullName());
$this->tester->seeInDatabase('users', ['name' => 'Miles', 'surname' => 'Davis']);
}