That's essentially correct.
A contract is where two people exchange promises to do something of value for the other person. Like if I promise to pay my handyman in exchange for promise to fix my shed. If one party does what they promised but the other doesn't, then it can go to court. A contract can be verbal, but written is best of course. The essence of the contract is the mutual understand that each will do what they promised.
A reward is an open offer by me to give something to someone if a condition is met. But I make that offer to the world in general. I can't have a contract with an unknown person. But I can still say that I'll give $100 to whoever finds and returns my lost dog.
A gift by definition is when one transfers something of value to another's ownership, with nothing in return. If there were something in return, then it would be a contract. No conditions or strings are attached. If there are any then it's not a gift.
A conditional gift is a loosely used term, and it usually only applies when an engagement breaks down and one party wants the ring back (because the ring is given as a gift on condition that there's a wedding), or in wills / estate law where a deceased will bequeath something if/when a condition is fulfilled, such as reaching a certain age.
So what you have here isn't really a conditional gift, nor is it a reward. It's certainly not a contract. The closest thing I can call it is fraud: you were led to believe that the other party had fulfilled a condition that's important to you (but not of value to you personally, thus not a contract) and on the strength of that lie you fulfilled your promise to make a gift. While some lawyers or judges might be fine to call it a "conditional gift", most won't because that's a term that has a specific meaning in estate law as I mentioned.
So I think you ought to do two things: try to raise the issue with the other person by email or text, don't get in their face, but see if by discussing this they admit that your intent to give a gift was based on them getting that degree. How to get her to admit these things? Well, that's up to you because you know the other party better than I. I will suggest that coming on strong and aggressive is likely to get their back up and you'll get no useful reply.
Then you might have criminal fraud, although I doubt that the police would do anything. This isn't a family law issue since you two aren't married and you weren't cohabiting, but the police would probably still view this as a civil matter.
Once you have had those discussions in writing, go see a lawyer who does civil and criminal law. Get a firm opinion as to whether you should pursue the laying of private information to a Justice of the Peace, who if satisfied that your evidence meets the burden of a criminal code offense likely having been committed, will order the charge laid. That gets around the police who probably won't take your complaint seriously.
If you decide not to try to lay the charge, you still can take them to court for the value of the car when you gave it, because your intent to gift was induced by their fraudulent misrepresentations. They lied to you in order to get something of value from you. That's a scam, and should be considered civil fraud.
But it will all depend on whether you have any evidence. Any evidence is better than none. Emails and texts between you, or a witness who will testify that this agreement was in place, those are good. Even if you can find someone who was aware of this promise and has personal knowledge that the other party was aware of it and understood it, that's still better than nothing.
But without any evidence to the contrary, yes the law assumes in this case that it was a gift. After all, you were in a relationship, so it's not too bizarre for a car to be gifted. If the other party was a complete stranger then that would be different story.
Even if you have no evidence, the other party doesn't know that. A letter from your lawyer might get an admission or agreement to return the car at least.
I hope that all makes sense. Please reply to me if there's more to discuss. If I've answered you then I'd appreciate a positive service rating please.