Is displaying a working Field Widget Form on its own possible? I'm interested in embedding a Field Widget Form out side the context of the whole node edit form. 

I have displayed full forms in the past using drupal_get_form but that doesn't seem to apply for solitary Field Forms. 

Is displaying a working Field Widget Form possible? What would be the best way to do so?

Both field widgets and "normal" forms seem very alike, so if this is not possible, what would be required to "change" a widget form into a normal form?

This question appears to be asking for something similar but I don't understand the answer.  That answer specifies using hook_field_widget_form_alter; what I don't understand is how to get the Field Form to be displayed not how to hook it once it is being created.
VBO does something like this in modify.action.inc:  

$form_key = 'bundle_' . $bundle_name;
$form[$form_key] = array(
  '#type' =&gt; 'fieldset',
  '#title' =&gt; $label,
  '#parents' =&gt; array($form_key),
);  
field_attach_form($context['entity_type'], $entity, $form[$form_key], $form_state, LANGUAGE_NONE);  


So, you need the entity type, the entity (which can be a blank object with just the bundle key set, that's what's actually used), the form where the widgets are added, and the language.
If you want to embed the widgets deeper into the form (not in $form, but in $form[$form_key] as I did, or even deeper), then that form array needs to have #parents set.

Of course, notice that this will embed the widgets of all fields belonging to that entity type &amp; bundle. This is how the attach functions were written.
Going around that would require you to reinvent quite a lot of code; see the actual code that does the heavy lifting.
What I do is go through field instances, get each $field_name, and if that field type doesn't interest me, I set $form[$form_key][$field_name]['#access'] = FALSE;
which hides those widgets from sight.

EDIT: Okay, ctools has ctools_field_invoke_field() which could in theory allow you to work on a per-field basis. I've never used it though. The text above is my direct experience.