Create a custom post type based on ‘Post’

If you created a new post type, it would behave like a post unless specified.

The problem you have is that the ‘post’ post type is built in. I suspect you want the other post type to simply be another type of post, and show up in the archives etc etc This isn’t possible with a custom post type, and the WordPress developers have stated in the past, if you want that sort of behaviour, just use posts, custom post types were not added for that purpose.

Instead it sounds more like custom post formats is a better choice for you. You can add your own post format, and add UIs for the different formats. Alex King built such a UI that shows different things depending on the different kind of format the post is:

http://alexking.org/blog/2011/10/25/wordpress-post-formats-admin-ui

But I’m afraid without further information about your context and why you asked this question, a satisfactory answer is not possible.