Yes each template can have its own DEFINE LINK_TO_PAGE section so the links can look different. However the Line_to_page defines what the link coming to a page looks like not the look of the links on that page.
You can override the look of links on a particular page by using the tag
[-- LINK template --] and specify the "template" name which contains the way you want the links to look.
This is all documented in the help. The general specification is found here
http://www.shopsite.com/help/10.0/en-US ... -page.html
And specific tag basic info can be found for each tag on the help page
http://www.shopsite.com/help/10.0/en-US ... .page.html
Here is the section that talks about changing the link look on a page.
[-- LINK template --] Create page link information by invoking the Link section of the target page and using the specified page template