In order to understand better these terms, let's check their definitions:
Length of Stay (LOS) Pricing:
It's a pricing strategy that accounts for the number of nights reserved and usually decreases the nightly rate for each night added. It allows customization on daily price and amount of guests.
Length of Stay (LOS) Discount:
It's a price discount system for guests who stay a preselected amount of days or nights. Length of Stay Discounts are used to encourage guests to book for longer periods of time than originally anticipated.
If we want to compare or link both of them, we could say that LOS Discount is a simplified version of LOS Pricing where you set a discount % for the daily price.
Is it better to use one or the other?
This will depend on your business model.
If you would like to offer different prices per day, offering better prices per night depending on the number of nights and also the number of guests, then you should use LOS pricing.
If you would like to offer a better price to the guest that books the property a minimum number of nights within a range, then you should use LOS discount.
Here is an overview of what some of the biggest sales channels support: