Here is the Template Hierarchy, which gives you an overview of the different approaches.
You could create for each category an individual PHP file:
- either
category-{CATEGORY ID}.php
- or
category-{CATEGORY SLUG}.php
.
Or you could use a single file category.php
in which you define the output (as well as its layout, style etc.) according to the current category – again, either depending on its ID or its slug.
Here’s a short example using the ID:
$category = get_the_category();
$cat_ID = $category[0]->cat_ID;
switch ($cat_ID) {
case 'A':
...
break;
case 'B':
...
break;
default:
...
}