De 13:1 If there arise among you a prophet, or a dreamer of dreams, and giveth thee a sign or a wonder,
De 13:3 Thou shalt not hearken unto the words of that prophet, or that dreamer of dreams: for the LORD your God proveth you, to know whether ye love the LORD your God with all your heart and with all your soul.
De 13:5 And that prophet, or that dreamer of dreams, shall be put to death; because he hath spoken to turn you away from the LORD your God, which brought you out of the land of Egypt, and redeemed you out of the house of bondage, to thrust thee out of the way which the LORD thy God commanded thee to walk in. So shalt thou put the evil away from the midst of thee.
In every context (there are only three) the dreamer of dreams is juxtaposed to "a prophet." Therefore, the dreamer of dreams would be the type of person who would tell everyone that "I HAD A DREAM" as if it were some wonderful thing everyone had to listen to.
It's kind of like during the time of Saul and David, they were called "Seers" but later they were called prophets. Both have a prophetic gift, but it manifests differently.
(Beforetime in Israel, when a man went to enquire of God, thus he spake, Come, and let us go to the seer: for he that is now called a Prophet was beforetime called a Seer.) (1 Samuel 9:9)
Numbers 12
5 And the LORD came down in the pillar of the cloud, and stood in the door of the tabernacle, and called Aaron and Miriam: and they both came forth.
6 And he said, Hear now my words: If there be a prophet among you, I the LORD will make myself known unto him in a vision, and will speak unto him in a dream.
7 My servant Moses is not so, who is faithful in all mine house.
8 With him will I speak mouth to mouth, even apparently, and not in dark speeches; and the similitude of the LORD shall he behold: wherefore then were ye not afraid to speak against my servant Moses?
A good contrast is what God says about how He communicated to people back then in contrast to how He talked to Moses.
From what I can tell, a Prophet has a way of communicating with God and is communicated to in dreams, and a dreamer of dreams only gets the dreams with no clarification or is not able to receive the communication from God.