Standard catalog as the name suggest is a typical product catalog and is be same for everyone. So each user gets to see same set of categories, products and skus. While the custom catalog facilitates catalogs in a way that different user can get the different information for the products or get altogether different products. Custom catalog allows to target a catalog to a specific user or group depending upon the business rules.
Also note that the standard catalog support is removed from ATG10 onwards so all you have is (custom) catalog only. Only ATG versions prior to 10, will have both standard and custom catalogs.
The standard catalog is the single catalog shown to all users. Each user sees the same set of categories and products.
The custom catalog allows us to create multiple catalogs which are intended to show differently to different users. We can target a catalog to a specific user or an organization depending upon the business rules.
For example, we can create a separate catalog for each country based on locale. Each locale will be having a separate catalog.