Inter vivos trusts are trusts created when the settlor is alive.
A declaration of trust is when one declares himself to be a trustee of his property for another. UTC § 401(2). No special formalities are required. (Though it is a bad idea to rely on an oral declaration of trust.)
The settlor can also be named as a beneficiary of the trust but not the only beneficiary or his titles would merge.
Unlike a deed of trust or an outright gift, a declaration of trust does not require delivery of the property. If something seems to be a gift but does not deliver the property, it might be a declaration of trust.
Inter vivos trusts are the most common and useful type of trust.
At common law, inter vivos trusts were presumed to be irrevocable.
Under the UTC, inter vivos trusts are presumed to be revocable unless declared otherwise. UTC § 602(a).