Difference between ABSPATH and TEMPLATEPATH?

ABSPATH refers to the directory in which WP is installed. TEMPLATEPATH refers to the current theme directory, or the parent theme directory if you’re currently using a child theme. Both are WP constants, so are not available in PHP outside WP.

As for bloginfo('wpurl'), it’s not the same as either one of them; it echoes a URL rather than a file path. (And anyway, if that’s what you’re actually trying to do, you should be using site_url() instead.)

Thanks for the explanation between ABSPATH and TEMPLATEPATH, but now I have another question…

Let say the directory of my WP installation is:
https://www.hello.com/wordpress/

what differences will it makes if I use,
include_once(ABSPATH . ‘wp-content/themes/posttypes.php’);
and
include_once($url = site_url(‘/wp-content/themes/posttypes.php’, ‘https’); echo $url;);

The difference, as Amy pointed out, is that the first one is a file path, and the second one is a URL. The result is that the first option will work, and the second will most definitely fail.