Is there a difference between factory unlocked and carrier unlocked?
Good question. 

Yes, there is a bit of a difference, though I largely agree with bmike. I guess I should add that while there might not be a difference in the outward functionality of the phone, there are differences between the phones provided by carriers, the procedure used to unlock those, and the unlocked iPhone sold by Apple. 

This past July, I went through the same unlock procedure that you did when my wife's parents gave her an iPhone 4S that was sent to them by AT&amp;T via an insurance policy that replaced a phone they believed was lost. Anyway, their phone was located right after the new one came in the mail, so they gave it to her. The problem was that we are on Verizon, so we couldn't use the phone. I wrongly believed it was the "world" iPhone that Apple sold, so I went through the process of getting AT&amp;T to unlock it. Unfortunately for me, I didn't pay close enough attention to the rear of the packaging, which clearly indicated that this was a GSM-only phone. Undaunted, I called the nearest Apple Store to arrange an exchange for a CDMA phone - a simple enough thing, right? After all, it was still in the shrink wrap. I spoke with the store manager, gave her the serial number of the phone, and was shortly informed that this was not a phone stocked by Apple stores. The kind of phone I had was marked to be sold only by AT&amp;T, either out of their retail establishments or shipping centers. I called AppleCare, and they informed me of the same thing. As it turned out, no one would even accept a brand-new, still-in-the-shrink-wrap, Apple iPhone 4S. Apple could not take it's own, brand new product in return for an essentially identical device. Only AT&amp;T could accept it as a return, and they obviously didn't have any CDMA capable phones to send in exchange. Ultimately we sent the phone back to my in-laws, and ended up purchasing our iPhone 4S devices directly through Verizon. 

To add to all this as sort of a general FYI, the unlocked iPhone sold by Apple is not the same thing as the "world" model, either. From Apple's Web Site regarding the unlocked iPhone:


  The unlocked iPhone includes all the features of iPhone but without a wireless contract commitment. You can activate and use iPhone on the supported GSM wireless network of your choice, such as AT&amp;T in the United States. The unlocked iPhone 4, iPhone 4S and iPhone 5 will not work with CDMA-based carriers such as Verizon Wireless or Sprint.


And here is the info for the "world" iPhone from the "tech specs" page:


  
  World phone  
  UMTS/HSDPA/HSUPA (850, 900, 1900, 2100 MHz);
  GSM/EDGE (850, 900, 1800, 1900 MHz)  
  802.11b/g/n Wi-Fi (802.11n 2.4GHz only)  
  Bluetooth 4.0 wireless technology
  


The reason for posting all of this is both as a response to your question and as a general information filter for prospective buyers.