BS2 vs BIAB calculator
 

BS states 6 gallons for a 6.25 grain bill on a 90 mash and boil while the BIAB calculator states almost 8 gallons, which one is right?

Check to make sure you have the similar inputs. What is the pre-boil amount you are looking for? Grain absorbtion for BIAB should be under 10% (if you squeeze well)

Is BS expecting a sparge? The BIAB Calculator does not.

You said 90 minute mash and boil. Do you have the same (90 minute) boil time entered into both "programs"?

Yes

BS2 pre boil goal is 5.6 gallons, going for 4 gallons into the fermentor

When I enter the values you've provided into the BIAB calculator I get a figure that is similar to what Beersmith is recommending.

That's we're I screwed up I thought the final volume meant the preboil volume.

To get rid of the sparge in BeerSmith, click on the full boil mash (BIAB) checkbox on the design page.

I'm having this same problem but I didn't see a checkbox for this on the design page. It's not there by default, you need to add it. In the lower right section of the design page, click the "select fields" and pick "full boil mash (BIAB)" and click save.

Also, don't forget to change your mash profile to BIAB or you'll get an error on the Mashout step