As Jim has noted, and as described in HELP, the Master Place List (MPL) contains unique entries of places, and each entry in the MPL has one and only one Place Style associated with it. All tags which refer to a given unique location actually simply point to that entry in the MPL. The Place Style is not associated with the tag, it is associated with the MPL entry. The tag just displays the information from that MPL entry. So if you change the Place Style in a tag pointing to that MPL entry, it changes in all the tags which point to that entry.
Unfortunately, it is not easy to see what Place Style is associated with an entry in the MPL, either from the MPL itself without viewing each entry, or from the partial list of the MPL which is displayed if you use the F2 key in a location field. To overcome/workaround this limitation, many of us users have adopted a convention of inserting a "code" which reflects information about this MPL entry (e.g its Style) in some Location field which its Style does not output. Thus such a code could tell you at a glance which entry has which Style so that you select the appropriate MPL entry. (But you would have to manually ensure that the code correctly reflected the Style of that entry.) If you do not use the first (L1/Addressee) location field, then placing a non-printing code in that field which also aids sorting can make the list provided by the F2 key more usable. For a further discussion of the use of such codes, search the archives for "F2 Key". You may find the following post here a good start at this discussion, and an example of using such a code for sorting in the TMG-L archives described here.
Hope this gives you ideas,