A Will (Last Will and Testament) is a document that, if properly executed, directs distribution of a person's assets after his or her death. The distribution is accomplished through a process called probate administration. See my upcoming post on who needs a Will and who does not.
A Trust is a legal entity that owns assets and manages and distributes these assets in accordance with Settlor's instructions, which are usually written out in a Trust Agreement. A Settlor (or Settlors, also sometimes called Grantor(s)) are persons that establish and fund the Trust, as well as establish terms of the Trust. Trust administration is a private process, as opposed to probate administration, which is public court record.
Probate (or Probate Administration) is a court-supervised process of distributing assets and paying debts of a person after their passing. The assets are distributed in accordance with the terms of that person's Will, or, if no Will was made, then in accordance with state law.