What is difference in functionality between turbo tax home and business 2017 and Home and business turbo tax 2017-with e-file?

I'm unfamiliar with "e-crater", but have reported your post to TurboTax moderators for investigation.  Is E-crater a reseller?  
Federal tax returns can all be e-filed.

website is: <a rel="nofollow" target="_blank" href="http://www.ecrater.com">www.ecrater.com</a> and search for turbotax 2017 home and business fed+efile+state for windows and mac

This has been sent to the Investigations Team at TurboTax.  But I'm inclined to think that this is NOT an authorized reseller.  I didn't visit the site, but ecrater.com appears to be a site to re-sell things.  I see something that refers to ecrater as a place to "get a free online store".  I would strongly recommend that you purchase your software elsewhere.

The Home & Business software is the Desktop (CD/download) platform, and it does include one free state tax prep program.  You will be required to pay to e-file your state return; federal e-file is free of charge.  

There are multiple online retailers, as well as brick-and-mortar retailers that are authorized to sell TurboTax products.  In addition to purchasing directly from TurboTax, you can purchase from Amazon, eBay, Office Depot, Sam's Club, Costco, and many others.  

Here's a link to the TurboTax webpage for this particular Desktop edition.  It looks like TurboTax current price (1/29/2018) is $109.99.  But shop around, as many other retailers do offer discounted prices.

https://turbotax.intuit.com/personal-taxes/cd-download/home-and-business.jsp

One additional note:  You can avoid the e-filing fee for the state return by printing and mailing your state return.

Sorry, I JUST re-read your post and see that you've already purchased from Amazon.  Good call.  I can assure you that the H&B product you'd receive (if you received anything at all) from e-crater would NOT be what you'd want.