The $wpdb->get_var() is a direct approach, to retrieve the value of a column, which is as straight-forward as it is stored in the database. The get_var() can be used to retrieve information from any column of any table in the WPDB context.
While, types_render_field() is a function particularly defined by Types Plugin's API, which retrieves information from a Types custom field only. Also, this function prepends 'wpcf-' prefix automatically, with the specified slug of the custom field. Since Types stores every custom field as 'wpcf-{field-slug}' in the database. This function also sanitizes the data, which is dependent on the type of the field.
If I understood correctly the only practical difference, willing to do the same thing, is that the types function sanitises the data.
Now, how can I use this types function in a php that exists outside the wp installation?
for example, for a get_var call I can load wp-load.php before.
Yes, you are right, for that particular matter - both can be treated as same, but types_render_field() does some extra work to ensure the sanity of the data.
Unlike WPDB class, you will have to make the plugin executable in a non-WP environment. In this case, you may need to strip several things off the plugin, or may need alter the plugin heavily.
I suggest taking a look at the code of the plugin and find the types_render_field() function for an understanding. You can also find the dependencies within the function itself.
However, I recommend using WPDB class for a non-WP setup, since this class is loosely coupled - so that it can be used with other setups.