BUG/CLN: datetimelike Index.equals may return True with non-Index
- [x] closes #13107
- [x] tests added / passed
- [x] passes `git diff upstream/master | flake8 --diff`
- [x] whatsnew entry

## [Current coverage](https://codecov.io/gh/pydata/pandas/pull/13986?src=pr) is 85.26% (diff: 87.50%)

> Merging [#13986](https://codecov.io/gh/pydata/pandas/pull/13986?src=pr) into [master](https://codecov.io/gh/pydata/pandas/branch/master?src=pr) will decrease coverage by **<.01%**

``` diff
@@             master     #13986   diff @@
==========================================
  Files           139        139          
  Lines         50562      50557     -5   
  Methods           0          0          
  Messages          0          0          
  Branches          0          0          
==========================================
- Hits          43116      43108     -8   
- Misses         7446       7449     +3   
  Partials          0          0          
```

> Powered by [Codecov](https://codecov.io?src=pr). Last update [59524af...580151a](https://codecov.io/gh/pydata/pandas/compare/59524af1e90d3dda2d885e711f7258704a020b6d...580151a16a4586728ef4315f45a64b2ad1a2dfd0?src=pr)
 Fixed impl and tests (added tests are not properly executed because it was overriden.

I'm still +1 to `.equals` should be `False` for non-`Index`, but there seems to be some tests which accepts `list` and returns `True`.

 So now I think we should keep current behavior for a while. Needs to decide whether to change it in future.
 lgtm. very minor comments. ping on green.
 @sinhrks Can you add some tests that explicitly test the behaviour for indexes with other attributes? (see my comment here https://github.com/pydata/pandas/pull/13986#discussion_r74693133) If it is not there yet of course.

I would also clarify this behaviour in the documentation.
 Further, I would say that changing Index.equals to return False with non-Index objects is an API change, and not a bug fix, so would add a note about that in the whatsnew.
 @sinhrks can you rebase
 thanks @sinhrks 
