If you are buying off-market or bringing deals to a buyer network, you will encounter both structures. The mechanics are simple; the differences that matter are practical.
Assignment
The original contract between seller and the contracting party is transferred to the end buyer for a fee. There is one closing. The end buyer takes the seller's place in the existing contract and completes the purchase.
It is the simpler and cheaper structure: one set of closing costs, one transaction, and the assignment fee is generally visible on the settlement statement.
Double close
Two separate transactions, usually on the same day. The intermediary buys from the seller, then sells to the end buyer as a distinct sale.
It costs more — two sets of closing costs — and requires funding for the first leg, though transactional funding exists for exactly this. It is used when the parties prefer that the spread not appear on a shared settlement statement, or when the original contract prohibits assignment.
What actually determines which is used
Whether the contract permits assignment. Whether the seller is a party that objects to it — some institutional and REO sellers do. Whether the end buyer's lender will accept an assigned contract.
It is a practical decision rather than an ideological one, and it is usually settled early.
The disclosure point
Regardless of structure, be straightforward about your role and what you are being paid. Concealment is what turns an ordinary transaction into a dispute, and in Illinois there are specific rules about wholesaling activity that are worth understanding properly.
This is a general explanation and not legal advice. If you are transacting regularly, have a real estate attorney review how you are structured.