The naming problem is real, and two of the three senses sit in the same regulation. "Cash back" names at least three different things, which is why the phrase alone is not enough to tell a reader what is happening to their money.
The first sense is the reward. Regulation Z's Official Interpretations, in comment 55(e)-2.ii.F, list among non-promotional communications a case where "a card issuer provides benefits (such as rewards points or cash back on purchases or finance charges) that can be applied to the account as credits, provided that the benefits are not promoted as reducing interest, fees, or other charges subject to § 1026.55." That is a benefit flowing to the account.
The second sense is the cash a cashier hands over on top of a purchase, and the same regulation's commentary treats it as the opposite kind of transaction. Discussing a point-of-sale transaction on a hybrid prepaid-credit card, comment 8(a)-9.iii.B describes a transaction that "partially involves the purchase of goods or services and partially involves other credit such as cash back given to the cardholder," and requires the creditor to disclose the entire amount as sale credit. So in the regulation's own words, cash back at a register is an extension of credit to the cardholder, while cash back on purchases is a credit to the account. Same two words, opposite direction of money.
The third sense is not a financial term at all. It is a verb followed by an adverb, as in pulling cash back out of a sweep account, and it happens to be spelled identically.
A fourth thing worth separating out is the cash advance, which is neither of the first two: it is a distinct product feature with its own fee, usually its own higher rate, and typically no grace period, so a cardholder who takes cash at an ATM is borrowing on the least favorable terms the card offers rather than receiving anything.
What the dollar denomination buys, stated precisely. The advantage of cash back is not that it is worth more. It is that its value is not a variable. A points balance has two numbers behind it, the count and the redemption rate, and the program sets the second one; a cash back balance has only the count. That removes an entire category of risk that applies to points programs, and it does not remove the risks that attach to the account rather than to the unit: a balance can still be forfeited on closure, and a program's terms still govern when and how a balance may be claimed.
The exception is the card that says cash back and pays points. Several programs credit a points balance redeemable for cash at a stated rate, commonly one cent per point. That arrangement is a points program with a dollar-shaped redemption option, and the rate is a program term. A reader who wants the structural advantage described above has to check which of the two they actually hold, because the marketing language is the same in both cases.
Redemption forms, and the ways they differ. Cash back is commonly taken as a credit against the statement balance, as a deposit into a linked deposit account, or as a check. Some programs also offer redemption into gift cards or merchandise, sometimes at a stated bonus and sometimes at a discount, which reintroduces a conversion rate the cardholder has to work out. Programs vary in whether a redemption is automatic, whether a minimum balance must accumulate first, and how frequently redemption is offered, and each of those is a term of the agreement rather than a feature of the product category.
Earn structures, and the conditions that come with the higher numbers. Three shapes cover almost every card. A flat rate pays the same percentage on everything. A category card pays a higher rate on named categories, fixed for the life of the card, and a base rate on the rest. A rotating category card pays a high rate on categories that change each quarter, usually requiring the cardholder to enroll each quarter and usually subject to a cap on the spending that earns the elevated rate. The conditions are where the arithmetic actually lives: an unenrolled quarter earns the base rate, and spending past a cap earns the base rate too, so the headline percentage describes a slice of the spending rather than the total.