If you open a subdocument from within a master document, the subdocument uses all the styles stored in the master document's template. If you open it separately and make style changes or apply a different template, your subdocument reflects those style changes as long as you're editing it outside the master document. However, if you save it, open the master document, and reopen the subdocument, you'll find that the master document's styles now take precedence wherever the styles conflict. If you insert an existing document into a master document, and the existing document is based on a different template, once again the master document's template takes precedence.
For more information about inserting an existing document into a master document, see "Adding an Existing Document to a Master Document," p. 672.
If you create a new style within a subdocument and later open that subdocument from within the master document, your new style is listed in the master document as well. However, if the style is based on a style that looks different in the master and subdocuments, text formatted with the new style may also look different depending on whether you're working on it in the master document or in a separate subdocument editing window.
Because this is complicated, here's an example:
Imagine that you're working in a subdocument that appears in its own editing window. You create a style named BookText and base it on the Normal style (which, by default, is 12-point Times New Roman). You add the extra formatting you want BookText to include: a first-line 1/2" indent and 8 points after each paragraph.
You now close the subdocument and open the master document that contains the subdocument. When you do so, the BookText style appears in your list of styles. Text formatted in the BookText style still has a 1/2" indent and 8 points after each paragraph. However, what if your master document used a different version of the Normal style, calling for text to be displayed in 11-point Georgia (instead of Times New Roman). Because your BookText is based on the Normal style, it would display your style in 11-point Georgia.
In other words, the elements you add to a style remain intact regardless of whether you display the text from within a master document or as a separate subdocument. However, where elements are based on another style, Word looks for that style in different places depending on how you are displaying the text. If you are displaying it as part of the master document, Word uses the underlying styles from the master document. If you are displaying it as a subdocument, in its own editing window, Word uses the underlying styles from the subdocument.
To learn more about based-on styles, see "Working with Based On Styles," p. 341.