The first screenshot in your question is not a public widget. The support SearchView (android.support.v7.widget.SearchView) mimics Android 5.0 Lollipop's SearchView (android.widget.SearchView). Your second screenshot is used by other material designed apps like Google Play.
The SearchView in your first screenshot is used in Drive, YouTube and other closed source Google Apps. Fortunately, it is also used in the Android 5.0 Dialer. You can try to backport the view, but it uses some 5.0 APIs.
The classes which you will want to look at are:
SearchEditTextLayout, AnimUtils, and DialtactsActivity to understand how to use the View. You will also need resources from ContactsCommon.
Best of luck.