Estimate Shipping not applying on the total of the shopping cart page

We are using version 4.40.0 and having the following issue in our shopping cart:

-When we ask the shopping cart to “estimate shipping” this gives us one price
-When we move to check-out where the “shipping method” box appears this gives us another price
-When we continue to check-out, the amount in the cart is pulled from the “shipping method” box

Has this issue been addressed and would it be fixed in the current version of the software.

We noticed this bug in the release notes for 4.50.0: #5907 Estimate shipping not applying on the shopping cart page

Has this been fixed in current version of the software?

I'm not sure we can assume that the "gives us another price" is related to not showing at all.
What shipping providers are you using?
I don't recall what information the "estimate" takes into account.  It could be that something is changing or is 'resolved' by the time you get further in checkout..  Discounts, etc.