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.
Inter vivos trusts are assumed to be revocable unless declared otherwise. UTC § 602(a).