Repo and Reverse Repo transactions are basically collateralized loans. As with any loan, the interest can be quoted as a fixed percent, or a spread to a reference rate.
In a Repo transaction, one is lending money to a dealer by buying a asset from a dealer and agreeing to sell the asset back to the dealer at a later date at a different price. The difference in prices represents the interest earned by the provider of funds to the dealer. In other words, the interest earned is embedded in the "repurchase" price.
A Reverse Repo is just the opposite. The dealer is providing a loan to the counterparty. The owner of an asset, sells the asset to a dealer at a price and agrees to buy it back at another price. The difference in the prices represents the interest that is paid to the dealer for borrowing funds.
The asset that is sold basically serves as collateral which the loan provider holds as security for providing the funds. The asset can be sold if the (close out) if the borrower fails to "repurchase" the asset from the fund provider (the "repurchase" is the repayment of the funds + interest).
With "general collateral", the asset doesn't have any "securities lending value" and therefore only serves as collateral for the loan. In this case, the dealer will ask a market rate for the loan (i.e. SOFR + spd, or an equivalent fixed rate) for the term of the loan. When it is open ended, it is basically an overnight loan, which can be rolled every day at the prevailing overnight rate.
When the asset has "securities lending value", the asset becomes special. Someone is looking to short the asset and willing to borrow the asset and pay the securities lending fees. As the dealer can now "lend the securities" and earn securities lending fees on the asset, they are eager to acquire the asset.
In order to induce the owner of the asset to Reverse Repo (reverse in) the asset to them, they will quote a lower interest rate to provide funds, or a negative spread to the reference rate (in extreme cases, the dealer may actually pay the asset owner by quoting a negative interest rate). The owner of the asset, can borrow funds at a sub-market rate and invest at a market rate and earn a spread.
The dealer can now lend the asset and earn securities lending fees, part of which is paid to the original owner of the asset in the form of a below market interest rate loan.
