Hi Abby! Congratulations on your upcoming purchase. Have you already negotiated a seller financing contract?
If this is new territory for you, I would strongly encourage getting a real estate professional on your team, be that a broker or an attorney. The legal and tax considerations of real estate contracts can be tremendous. Depending on your state (I am not familiar with Colorado), you will likely work with a title company or an escrow attorney to manage the critical closing documents and to consummate the sale.
There are a lot of contracts which are negotiated and enforced outside of the closing, related to the inspection, due diligence, surveys, appraisals, etc. If you aren't working with a real estate pro who is tracking these for you, you will need a secure system for storing these. Digital copies are only acceptable if the digital signing systems meet certain electronic signature requirements. Otherwise, keep your original wet-signed copies and guard them.
If you do happen to negotiate seller financing, you will absolutely want an attorney to draft/review the documents related to this private loan and also consult with your CPA. To answer your question, you will take ownership, even with private financing, however, there will be a recorded deed of trust in the name of the seller. If the seller is not financing the full purchase amount, you'll need to fully disclose this to an additional lender whom you engage with. There is certain positioning on the note that says who gets the first chance to foreclose in the event of default. Odds are an institutional lender will not be okay sitting in the second seat. Also, do not let the seller write a second contract nor side arrangement to help you get a mortgage for part of the purchase and seller carry for the rest. This is mortgage fraud.
In closing, engage the help of a professional. A good broker will negotiate their commission from the seller and your representation will be paid by the seller. I've been contacted by buyers before who executed contracts with sellers which were on personally drafted sales contracts, which stripped the buyers of their protections and heavily favored the seller. One such person ended up on the hook for all closing costs, her earnest money was non-refundable on day one, she signed away her right to ask for any inspection related repairs, and took possession of the property by quit claim deed. Scary stuff!