No board and no adviser is the structural fact everything else follows from. A mutual fund has directors who hire and supervise a manager, and the manager trades the portfolio. A unit investment trust has neither. The SEC's investor education puts it plainly: a UIT "does not have a board of directors, corporate officers, or an investment adviser to render advice during the life of the trust". So there is no one whose job is to react to news, rebalance after a run, or sell a deteriorating holding. That is a limitation and a design choice at once, and the SEC frames the upside in the same passage: because the portfolio is generally fixed, "investors know more or less what they are investing in for the duration of their investment", and the securities are listed in the prospectus.
Fixed, redeemable and finite are three separate features, and it is easy to collapse them. Fixed means the trust buys a relatively fixed portfolio and holds it with little or no change. Redeemable means the trust will buy an investor's units back at approximately net asset value, which is a mutual-fund feature rather than a closed-end one, and many sponsors additionally maintain a secondary market in units at market prices. Finite means the trust terminates and dissolves on a date specified when it is created; the SEC gives the example of a bond UIT whose termination date may be set by the maturity of its bonds, and notes that when the trust terminates the remaining portfolio securities are sold and the proceeds are paid to investors.
Because the units are redeemable, the pricing rules follow the mutual fund rather than the closed-end fund. The SEC states that mutual funds and unit investment trusts generally must calculate net asset value at least once every business day, typically after the major U.S. exchanges close. A closed-end fund, whose shares are not redeemable, is not subject to that requirement. What the number is and how it is computed belongs to the page on net asset value; the point here is that a UIT is on the daily-calculation side of the line.
The classification has one consequence that surprises people, and it concerns exchange-traded funds. Rule 6c-11, the SEC's 2019 ETF rule, defines an exchange-traded fund as "a registered open-end management company" meeting further conditions. A unit investment trust is not a management company, by the operation of section 4(3), so a UIT-structured exchange-traded product cannot rely on that rule. It does not follow that such a product is not an ETF. The SEC says the opposite in two places: its investor glossary states that ETFs "are registered with the SEC as open-end investment companies or unit investment trusts under the Investment Company Act of 1940", and the adopting release for Rule 6c-11 says the SEC was not rescinding the exemptive relief of UIT ETFs, which are "outside the scope of rule 6c-11". Products organized that way operate under their own exemptive orders rather than under the rule.
One more place the class shows up by name. Rule 12d1-4, which permits funds to invest in other funds beyond the statutory limits, has a condition written specifically for this structure: where the acquiring fund is a unit investment trust, its principal underwriter or depositor, rather than an adviser or a board, must evaluate the complexity of the arrangement and find on or before the date of initial deposit that the trust's fees and expenses do not duplicate those of the funds it holds. The rule has to name the UIT separately precisely because there is nobody else in the structure to make the finding.