get_theme_file_uri(), get_theme_file_path(), get_parent_theme_file_uri() and get_parent_theme_file_path() are relatively new (introduced in WordPress 4.7) functions that have a couple of significant advantages over using get_template_directory().
get_theme_file()andget_theme_file_path ()allow you to reference files in your theme in a way that allows them to be replaced by a child theme. This lets you do things like allow images to be replaced, which wasn’t previously possible (without a custom function).- They are all filterable, which allows child themes and plugins to replace them with files either outside a theme, or with files that aren’t in the same directory as they were in a parent theme. The filter would also let you prevent the inclusion of a file entirely.
The functions that end in _path() return the path to the files, so would be used for including files for use on the server, while the functions ending in _uri() return the URL to the file, for use on the front-end.
The _parent_theme_ functions let you reference files without letting them be replaced by a child theme.
Since the introduction of these functions the only reason you would use the template_directory or stylesheet_directory functions would be to just get the URL or path to the directory itself.
You shouldn’t need to ever use the TEMPLATEPATH constant.