Let me use a source that explains it in more detail than I can, although sorry for its length:
On the one hand, the Talmud does explicitly state that Daniel was not a prophet.1 On the other hand, when the Talmud states that only 48 prophets and 7 prophetesses prophesied to Israel,2 the sages disagree as to whether Daniel is included in that list or not.3
What is even stranger is that the remark in the Talmud that Daniel was not a prophet is made in connection with an incident in which Daniel seems to have seen a vision, when the three official prophets who were with him did not:
And I, Daniel, alone saw the vision, but the men who were with me did not see the vision. But a great quaking fell upon them, and they fled into hiding.4 Who were these men? Said Rabbi Yirmiyah, and some say it was Rabbi Chiya bar Abba, They were the [prophets] Chaggai, Zechariah and Malachi. They were superior to him [Daniel], and he was superior to them. They were superior to him, in that they were prophets and he wasnt. He was superior to them, in that he saw the vision and they did not.5
We must therefore conclude that what distinguishes someone as a prophet is not whether he or she has visions, but something deeper and more fundamental.
While in common parlance the word prophecy is used to describe visions in general, in truth there are two different kinds of visions: prophecy and ruach ha-kodesh (Hebrew for divine inspiration). With prophecy, it is almost as if one sees the revelation, gaining an intimate familiarity with the divine, while ruach ha-kodesh is more of a detached, factual kind of knowledge, as shall be explained.
Some prophets see a vision or dream of an angel speaking to them; others see the form of a man, or may perceive that G‑d Himself is speaking to them. And yet others dont see anything; they only hear the prophetic words addressed to them. The prophet may experience that which is heard with the greatest possible intensity, just as a person may hear or perceive a storm or an earthquake. Or the prophet may hear the prophecy as ordinary speech.6
There are many different levels and types of prophecies,7 but the common denominator between them is the way the prophets intellect merges with the divine and transcends the normal powers of the intellect. Thus, when prophets are granted an intimate familiarity with the level of divinity that has been revealed to them, their bodies weaken and tremble and their regular senses become confused or paralyzed, or they simply fall asleep. It is for this reason that we sometimes find that the prophet is referred to in the scriptures as one who is acting irrationally.8 This is not because the prophet lacks wisdom. On the contrary, he or she is connected to G‑ds wisdom, which transcends human intellect. Rather, it is because during prophecy, the people observing the prophet perceive only the void of what they consider to be rational intellect; they do not, however, perceive how the prophets mind has transcended the normal human intellect and is merged with the divine.9
Those who have ruach ha-kodesh, however, feel as if the divine spirit came upon them. With it they receive a new power that encourages them either to take a specific action, speak wisdom, compose hymns, exhort their fellow men or discuss political or theological problems. All this is done while the one with ruach ha-kodesh is in full possession of his or her senses.10
It is true that the inspiration may sometimes come in the form of a dream, as it does with prophets. There is, however, a difference between the visions experienced by prophets in a dream and those that come through ruach ha-kodesh, as was the case with Daniel.
The difference can be seen in how prophets and those inspired by ruach ha-kodesh refer to their visions and dreams. When prophets prophesy, they are informed that the vision was a prophecy, and upon awaking, they state decidedly that it was a prophetic experience.11 For example, when Jacob awakened from his prophetic dream of the angels ascending and descending the ladder, he did not say that it was a dream; rather, he proclaimed (Genesis 28:16), How awesome is this place! This is none other than the house of G‑d, and this is the gate of heaven. And he later referred to the incident by saying (ibid. 48:3), Almighty G‑d appeared to me in Luz, in the land of Canaan, and He blessed me.
Daniel, however, used the language of visions to describe his experiences, even after he saw angels and received knowledge through them, as we can see from the following verses from the Book of Daniel:
Then the secret was revealed to Daniel in the vision of the night (2:19).
In the first year of Belshazzar, the king of Babylon, Daniel saw a dream . . . (7:1).
. . . and the visions of my mind terrified me (7:15).
So while it is true that Daniel had visions, they were on the level of ruach ha-kodesh, divine inspiration. Therefore, the book of Daniel was made part of the biblical section of Ketuvim, the Writings or Hagiographa, and not the Neviim, Prophets.12
When discussing the difference between prophecy and ruach ha-kodesh, a distinction needs to be made between the levels of the divine revelation (how high in the chain of emanation between G‑d and man the individual reaches) and the quality of the revelation (how intimate and clear the revelation is to the individual).
While the quality of the revelation is much greater in prophecy than in ruach ha-kodesh, the level of revelation reached through ruach ha-kodesh can be much higher than that reached through prophecy. Since the prophet gains an intimate knowledge and familiarity with the level of divinity that is being revealed to him or her, to the point that we say that the prophet saw G‑d, there is a greater limit to how high of a level of emanation the prophet can see, as G‑d told Moses, No man can see me and live.13
With ruach ha-kodesh, however, it is not as if one actually saw or heard something; rather, it is similar to perceiving something with the mind. Therefore, the recipient of this ruach ha-kodesh may sometimes be privy to greater knowledge of the myriad levels and layers of divine emanation than even the prophet. For the knowledge received through ruach ha-kodesh is similar to the cataloging of facts, the names of the different spiritual worlds and the rules by which they interact. But in the end, he knows only the fact of their existence (yediat ha-metziut), but he has no real appreciation of their true nature, for he has never seen it.
This is what the Talmud means when it proclaims that a sage is superior to a prophet.14 For the sage, through ruach ha-kodesh, can be privy to levels of insight that surpass that which the prophets are able to envision tangibly. And while the sage grasps only facts, nevertheless it is divinely inspired knowledge of the facts.15
The levels of prophetic revelation experienced throughout a prophets lifetime are, however, not static. The same prophet can at times experience different levels of prophecy, ruach ha-kodesh, or both.16 Therefore, even if Daniel had attained the level of prophecy at one point in his life,17 it was not in relation to the book of Daniel, which is therefore still considered part of the Ketuvim, the Writings. --http://www.chabad.org/library/article_cdo/aid/1735365/jewish/Why-Isnt-the-Book-of-Daniel-Part-of-the-Prophets.htm
. Daniel is also in the writings, for "Jewish" (not necessarily bizarre) reasons. To argue with a Jew about whether or not Daniel was a prophet, you simply need to:
