When you run tests in Eclipse on project level (or package level), Eclipse searches all project's source folders for JUnit classes (or selected package). These are all classes with @Test annotations and all classes with @RunWith (probably some more too). Then for all these classes it runs them as tests.
As a result of this behavior, if you have a suite class that references tests classes in the same project, these tests will run twice. If you had another suite that did the same, they would run three times and so on. To understand this behavior try running a suite that contains one test case twice, for instance:
@RunWith(Suite.class)
@SuiteClasses({ TestCase1.class, TestCase1.class })
public class TestSuite {}
Accepted strategy here is to define a suite or suites for a project an run them exclusively. Do not start tests on a project level but run selected suites only.
As far as Maven is concerned, I suspect that its default configuration only picks out suite class and omits test cases. Had it been configured differently, it would behave the same as Eclipse.