Rails has a handful of test classes. ActiveSupport::TestCase, ActionController::TestCase, ActionView::TestCase, and ActiveDispatch::IntegrationTest. The latter three inherit from ActiveSupport::TestCase.
In Rails 3.x, ActiveSupport::TestCase inherits from Test::Unit::TestCase
In Rails 4.0, ActiveSupport::TestCase inherits from MiniTest::Unit::TestCase
In Rails 4.1, ActiveSupport::TestCase inherits from Minitest::Test
On Ruby 1.9 and 2.x, Test::Unit::TestCase inherits from MiniTest::Unit::TestCase.
So, if you are on a modern Ruby and a somewhat modern Rails you are already using Minitest.
minitest-rails is a replacement for the default Rails testing engine that enables Minitest features like the Spec DSL that Rails disables by default. That's it. You get some new options in the generators to support the Spec DSL. And you some new rake tasks.