Federal regulation names the product outright. 12 CFR 204.2(d)(2) provides that the term savings deposit also means a deposit or account, such as an account commonly known as a passbook savings account, a statement savings account, or as a money market deposit account, that otherwise meets the savings-deposit requirements and from which the depositor may make transfers and withdrawals to another account or to a third party, regardless of the number of such transfers.
But the tidy conclusion that an MMDA is legally a savings account rather than a checking account is an overstatement, and almost nobody says so. The same regulation defines a transaction account at 204.2(e), and (e)(2) sweeps in deposits on which the institution has reserved the seven days' notice right and that are subject to check, draft, negotiable order of withdrawal or other similar item, expressly including accounts described in paragraph (d)(2), which it then names in parentheses as savings deposits. So an MMDA that comes with checks is a savings deposit under (d)(2) and a transaction account under (e)(2) at the same time. The hybrid is legal as well as commercial.
Regulation D's six-transfer limit was deleted, not paused, and both of the usual summaries mislead. The Federal Reserve Board amended the regulation in 2020 to delete the six transfer limit from the savings-deposit definition, and the current text of 204.2(d)(2) permits transfers and withdrawals regardless of their number. But the Board's change permits rather than requires institutions to stop enforcing their own limits, and many still do, charging an excess-withdrawal fee under the account agreement. So "federal law limits you to six a month" is wrong, and "the limit was removed" is wrong for anyone whose bank kept one. The question to answer is what your own fee schedule says. That fact is more strongly associated with money market accounts than with plain savings, because the payment features make the limit easier to hit.
Tiered pricing is the practical catch, and it is where the advertised number stops being the number you get. Money market accounts are commonly priced in balance bands, so the headline annual percentage yield attaches to balances above some threshold and the rate below it can be a small fraction of that. Regulation DD requires an advertisement quoting a rate of return to state it as an annual percentage yield and to disclose the conditions attached, including any minimum balance, which is exactly where a tier is disclosed. Read the tier table rather than the headline, because on a modest balance a plain high-yield savings account with a single flat rate can pay more than a money market account advertising a higher one.
What remains is the ordinary comparison. Against a savings account, a money market account adds payment features and often a higher minimum balance. Against a checking account, it pays interest but is not designed for the volume of transactions a checking account handles. Against a certificate of deposit, it keeps the money reachable and gives up the fixed rate, since a money market rate is variable and the institution can change it at any time. Interest is ordinary income in the year it is credited and arrives on a Form 1099-INT.