The main difference between JUnit and TestNG is the test class instantiation. JUnit always creates a new instance of the test class for each test method run. TestNG only creates one test class instance and then runs all test methods of this instance.
The JUnit approach guarantees the independency of all test methods. It just does not matter, in which order they run. Additionally, all instance fields are always setup the same for each test method. Initializing data, that is common for all test methods, must take place at the class level, thus it must be static. This is the reason, why the @BeforeClass method must be static.
The TestNG approch does not guarante the independency. In fact, you cannot use an instance field in the same manner as in JUnit tests. If you change such a field in one test method, the changed value is still observabl in another test method. However, this behavior has also an advantage: Sometimes there are dependencies between some test methods. With TestNG, a tester can express them.
Because of the one-instance-approach of TestNG, the @BeforeClass setup can also be a non-static method, but it is still run only once. It was a design decision, but testers using TestNG must be aware of that.