What is the difference between a Offer to Purchase Real Estate and a Purchase Agreement? Which would qualify as a "signed contract to make a purchase"? Are both used prior to closing or do you choose one or the other?

The answer is contained in the words of your own question.

An "Offer" is uni-lateral . . . . involving action by only one Party.

An "Agreement", or Contract, is at a minimum, bi-lateral and involves at least two Parties.

An Offer can become a Contract when a second Party signs, or agrees, and makes it a Contract.

Thanks so much for the clarification. So the Offer to Purchase can serve as a legal "contract to purchase" once signed by the second party (seller)? Do real estate agents typically have both parties complete a purchase agreement as well or does the Offer to Purchase typically serve as a binding contract until closing?

Some States have local customs and procedures requiring (or allowing for) a two(2) step process involving a short "Binder" which is a temporary until the Parties can complete a full Purchase and Sales Agreement.

By it's very name, you can see that a "Binder" is also a binding Contract between the Parties; but it is abbreviated and will typically be of limited duration (or temporary) until a complete Contract can be drafted and signed by the Parties. Binders are fine; but many deals subsequently die while trying to flesh out the details of a complete Purchase and Sales Agreement, including all terms and conditions . . . . leading us to often repeat that "the devil is in the details".

Check with your local Georgia authorities to see how the process is typically handled there. I'm only speaking generally.

I sincerely appreciate your concise and easy to understand answer. Thanks so much!