Customer pricing groups (available with the basic version) and detailed pricing (available with the premium version) are two different ways of applying customer pricing to products.
Applying customer pricing through customer pricing groups involves creating a group, selecting a group of products, then assigning a discount for each pricing tier within that group for those products. Different discounts for different products would require separating those products in their own customer pricing group.
The detailed pricing functionality allows for easier management of individual products and their respective discounts compared to using customer pricing groups. Products and customer pricing tags are listed in a grid type format and you're able to specify the fixed price or discount for a particular product or variant. This is especially helpful in the situation where each product or variant has its own discount percentage or fixed price.
Another advantage is that all products are isolated from each other (unlike with products in customer pricing groups) updating one variant/customer tag discount only causes the app to process that one product, instead of all of the products that happen to be in a customer pricing group.
Note: Detailed Pricing discounts will apply ahead of Customer Pricing Group discounts.