Sorry for the confusion.

If they do not conflict with the styles that are in the current document, the styles in the normal template are available. Styles with the same name in the document will be used, not the ones in the normal template.

With other global templates, absent some other method of transfer, the styles in other global templates are simply non-existent for open documents and other templates. See A Global StyleSheet in Microsoft Word?

Giving context to the information on the hierarchy of templates:

First, look in the document.

Any styles in the document will be used in preference to others if they have the same name.

Next, check the attached template. Any macros or styles in the attached template will take priority over any except those of the same name in the document.

Any styles changed in the template after the document was created will be available as changed to the document by updating styles. Absent such updating they will not be available.

Then check the Normal template (Normal.dotm or Normal.dot).

All styles in Normal.dotm / Normal.dot are available to all documents. Those styles already in the document will not take on the attributes of styles in Normal.dot unless you update them. (Normal.dot has many more styles than are ever used in one document.)

EDIT: SEE NEXT POST FOR CORRECTIONS