Before I get to my comments, I would like to point out a couple things relevant to this discussion that will be helpful for us to keep in mind. First, that credit card underwriting criteria can change at any point,second, that it is possible the factors impacting your score have been updated since your last score pull, and finally, in addition to the possibility that each credit bureau may have slightly different information on you, the standard FICO-like score models from the three major credit bureaus are all slightly different, resulting in differing scores from each.
Regarding the pre-approved application, is the application indeed "Pre-Approved" and not "Pre-Screened"? There is a significant difference between the two based on what I [think I] know of regulations pertaining to credit offers. I don't currently have a link to the specific location in the FCRA that mentions these two types of offers, but from what I previously read, I believe one of the two is mandated a very high approval rate and another a moderately high approval rate like 85% and 55%. That being said, the likelihood of you being approved for the Discover card in your offer could range from ok to very good based on the offer type. Do remember though, the information on the credit pull used for the pre-screened/approved offers may not be reflective of your credit characteristics at the time of your application. In addition to checking your credit when you apply, I also recommend you, or someone you trust, to go through the FCRA section regarding this prior to making your decision to apply for the card. I have included a link to the pdf contained on the FTC website: http://www.ftc.gov/os/statutes/031224fcra.pdf
Empirically, it seems like the Discover Card you mentioned is marketed to the Prime level borrowers; which are commonly defined as those near or above 700 or 720. The Chase Freedom card also appears to market to this group. I personally don't feel very comfortable applying for cards until I know I have a very high approval rate, or am getting into the targeted score range. There are some other cards that are supposed to target people with average to above average credit scores such as a couple I have listed here. I am sure that there will be other forum members posting a few card recommendations for the score range as well, so please do shop around.
Capital One Cash Rewards for Average Credit: Cash Back Card, $39 Annual Fee
Capital One Classic Platinum Credit Card: 0% intro Rate Card, $39 Annual Fee
Barclaycard Rewards Mastercard: Rewards Card, No Annual Fee
At least a few others not mentioned here as well
*Remember that typically, the better the offer is the harder it is to get the card!
Good work taking a look at your score before applying for your next card as that is a very important aspect of managing your credit. Keep up the good work and let us know how it goes!