Different post views for different category views

For styling archive index pages for a given category, target body.category-slug (where slug is the category slug) in CSS.

For styling single blog posts that have a given category, assuming your post container is a div, target div.category-slug (where slug is the category slug) in CSS.

For PHP operations, you can also use is_category( 'slug' ), which returns true if you are on the archive index page for a given category, and you can use in_category( 'slug' ) which returns true if the current post is in a given category.