The attribution window determines which value gets credit for a particular success event.
The date range determines when the success events happen.
Say for example I have a 30 day attribution for evar1, we'll call it search term for this example.
Day 1 - search for hats
Day 10 - search for shoes and place an order
Day 18 - search for shirts
Day 29 - place an order
So, my attribution window is going to look at the success event, order, and based on the allocation determine which values to give credit to. Let's say my allocation is "last touch." That means my first order gives credit to the search for "shoes" and my second order gives credit to the search for "shirts." Those are determined by the allocation and the lookback window being 30 days.
If my lookback window was only visit, the first order would still give credit to "shoes" but the second order wouldn't give credit to anything, because the search term expires at the end of the visit, and there was no other search in the same visit as the order.
Now, when you put a date range in your dashboard, whether it's the panel date range or one of the purple ones you apply to a table, that determines what data we return. If we have a date range that covers the entire 30 day period, our table would look something like
Search Orders
shoes 1
shirts 1
But if our date range only covers the last 10 days our table might look like
Search Orders
shirts 1
The date range isn't determining what values get credit, it's only determining what is displayed in your table. For the second order, the search for shirts happened before the 10 day time period we're using for our table, but the value persisted and was given credit when the order was placed. The date range is looking at those success events and saying, what success events happened in this time period? That's what it is returning.