When you set up a counter for a page, the look, size, and color will be the same no matter what web address is used to access the page, however the count displayed may be (and most likely will be) different.
For example, if the file index.html has a counter installed on it, the counter will display a different count depending if the file is accessed using http://www.your_domain/index.html or http://your_domain/index.html.
As part of the counter setup, you can define a "Preset Counter Value," and, as an advanced option, you can use this to preset counters based upon the web address. Just select the web address under Advanced Option before completing the three steps.