Rationalize mojo_public_*tests targets.

mojo/tools/data/unittests

 # This file contains a list of Mojo gtest unit tests.
 # This must be valid python. It can use the |config| global that will be a
 # mopy.config.Config object and must set a |tests| global that will contain the
 # tests to run.
 # TODO(vtl): Add a way of specifying data dependencies instead of cacheable.
 
 tests = [
   # EDK tests:
   {
     "test": "mojo_edk_base_edk_unittests",
   },
   {
     "test": "mojo_edk_embedder_unittests",
   },
   {
     "test": "mojo_edk_platform_unittests",
   },
   {
     "test": "mojo_edk_system_unittests",
   },
   {
     "test": "mojo_edk_system_test_unittests",
   },
   {
     "test": "mojo_edk_util_unittests",
   },
 
   # Public tests:
   {
-    "test": "mojo_public_bindings_unittests",
-    "cacheable": False,
-  },
-  {
     "test": "mojo_public_c_bindings_unittests",
   },
   {
-    "test": "mojo_public_environment_unittests",
+    "test": "mojo_public_c_system_unittests",
   },
   {
-    "test": "mojo_public_system_unittests",
+    "test": "mojo_public_cpp_application_unittests",
   },
   {
-    "test": "mojo_public_utility_unittests",
+    "test": "mojo_public_cpp_bindings_unittests",
+    "cacheable": False,
+  },
+  {
+    "test": "mojo_public_cpp_environment_unittests",
+  },
+  {
+    "test": "mojo_public_cpp_system_unittests",
+  },
+  {
+    "test": "mojo_public_cpp_utility_unittests",
   },
 
   # Non-system, non-public tests:
   {
     "test": "base_unittests",
   },
   {
     "test": "crypto_unittests",
   },
   {
@@ skipping 61 matching lines @@
       "cacheable": False,
     },
   ]
 
 if config.target_os == config.OS_LINUX:
   tests += [
     {
       "test": "sandbox_linux_unittests",
     },
   ]