Where an account is opened and who manages it is secondary to what the account really is. A Money Market is a type of savings account defined by the FRB's Reg D.
https://www.bankersonline.com/regulations/12-204-002 Once on the page, search on "money market."
When you have an account meeting this definition, the rules apply. Reg DD will apply as to disclosures and conditions for consumer accounts and Reg O is typically a lending related regulation but is impacted by deposit products in overdrafts and in some cases interest payments to insiders based on the deposit account.
Trust account requirements can add another layer of requirements to these deposit accounts. I cannot speak to them, however.