Hi,
The "price" choices use the prices that you set in the products and dynamically retrieve them. So it can take into account price restrictions like user group, dates, etc. However, it's quite taxing on the database as it complexify the query to load the products quite a lot.
The "sort price" choices use the "product_sort_price" column of the products for the sorting. That column is filled by HikaShop automatically when you save the product or its variants in the backend interface. It only take into account unit prices of the main currency. Since the value is precalculated, it doesn't add any complexity to the query to load the products on the frontend. On top of that, it also allows you to set the value to whatever you want via the database, mass actions, or CSV import.
So both options can be useful based on your needs.
Regarding the text of the sort price sorting, you can use translation overrides:
www.hikashop.com/forum/filters-search/89...t/309141.html#309147