When using 'Percent Off' and 'Price Off'  Discount Methods, the discounts are calculated from the product's 'Sale Price' section (not the​ compare-at-price).
However, You can also use the 'New Price' Discount Method to set final discounted prices for the customers, but the 'New Price' must be less then the regular product price (not the​ compare-at-price).

CLICK HERE to learn more about the Discount Methods.

Here is a quick example: 

Example: Customers tagged 'Wholesale' get 10% off.

Price : $50 [also known as Sale Price]
Compare at price : $60
The discounted final price on this product would be:
=> $50 at a 10% discount = $45 [discounted price] 

Options to display cross-out price beside the discounted price. 

Option #1:  Display 'Sale Price' $50 as cross-out price: [Default Option] 
New Price:  $45  $50

Option #2:  Display 'Compare at price' $60 as cross-out price: 
New Price:  $45  $60

Note: In this option, the 'Compare at price' will show as cross-out price on home, collection, product, search and cart pages. However on the /checkout page the 'Sale Price' will appear as cross-out price instead of 'Compare at price' as cross-out price.

How to change settings for Cross-out price:

By default 'Sale Price' appears as Cross-out price. If you want to  display 'Compare at price' as Cross-out then please enable it from the application settings: 

Note:
Discounts can not be specifically set from the 'Compare at price' only.