Secret Trusts vs. Semi Secret Trusts

Both secret trusts and semi-secret trusts fall under the larger category of testamentary trusts. You'll know you're dealing with a testamentary trust if there's a will involved. Unlike with an inter vivos ("among the living") trust, a testamentary trust is one in which the intent of the trust and the essential terms of the trust must be ascertained from the will itself, from a writing incorporated by a reference to the will, or from the exercise of a power of appointment created by the will. Simply, look out for a will in which property is not left outright to a beneficiary of the will as might normally be the case, but is instead left to a trustee to do all the things that a trustee does with the property for the benefit of the beneficiaries.

Secret Trust: A will might make a gift which appears to be an absolute gift but was in fact made in reliance on the will beneficiary's promise to hold the property in trust for another. The way this might show up on an exam is that someone might contest the will by presenting extrinsic evidence that the will beneficiary promised to hold the property in trust for another. If the promise is proven by clear and convincing evidence, a constructive trust will be imposed on the property such that the will beneficiary will be deemed a trustee so that the only power granted to the will beneficiary over that property will be to hold the property in trust for the intended beneficiary. Note that it's irrelevant whether the promise was made before or after the will was created; in either case, a constructive trust may be imposed.

Semi-Secret Trust: A semi-secret trust is even a bit more straight forward than a secret trust. In a semi-secret trust, the will makes a gift in trust to a named trustee but fails to name any beneficiary. Without any named beneficiary there can be no trust and so the gift fails. Here, unlike in the above, a constructive trust will not be imposed. Rather, the named trustee holds the property on a resulting trust with the only obligation to ensure that the gift is transferred to the testator's heirs.

I should add that it's tough to really figure out why this second type is called a "semi-secret" trust. But that's not important; just know how it differs from a secret trust, and how each might apply to a given set of facts.