acf/save_post is called with the post ID of the post being saved. For more information on this https://www.advancedcustomfields.com/resources/acf-save_post/.
You can get the post type like this
$post_type = get_post_type($post_id);
if ($post_type == 'your-custom-post-type-slug') {
// do something for this post type
}
All field in all groups included in the form are submitted and all are in $_POST[‘acf’] and do not include any additional information that tells you what group they are in.
I’m not sure what you mean in your reference to taxonomies.