Is a denial of discharge different than a debt being non-dischargeable?

Yes, exactly.  A denial of discharge is a very bad thing indeed.  In a nutshell, the debtor is told that he is not getting any discharge of his debts and will remain liable for repaying the full amount of ALL of his debts.  A Bankruptcy Court can deny your discharge as a response to certain bad behaviors on your part, such as if you (the debtor) fail to take the required financial management course, make false statements under oath, conceal property that should have been part of the bankruptcy estate, or fail to obey a lawful order of the court.

As you stated, a determination that a debt is not dischargeable deals only with one specific debt.  For example, the bankruptcy court may notify you that your student loans are not dischargeable.  In that case, your bankruptcy case will move forward and all of your other debts may still be discharged.  I always recommend that people hire a bankruptcy attorney rather than trying to handle their case on their own.  This stuff can be confusing.  Good luck.