It appears that when one utters a prophecy it could apply to both preaching and teaching. In an broader sense, prophesying means that one serves as a mouthpiece for God.
I speak as one who grew up in the Pentecostal/Charismatic movement and I know there was a huge emphasis of prophetic foretelling. But both the Hebrew scriptures and the NT prove prophecy to be far more nuanced.
In Luke Jesus refers to Abel as a prophet who was slain:
Luk 11:50 that the blood of all the prophets, which was shed from the
foundation of the world, may be required of this generation; Luk
11:51 from the blood of Abel unto the blood of Zachariah, who
perished between the altar and the sanctuary: yea, I say unto you, it
shall be required of this generation.
There's debate concerning in what manner Abel was a prophet. But most Bible students will agree that righteous Abel's offerings of sacrifices and subsequent murder prophetically pointed to the Messiah. In Abel's case prophetic utterances may not have been made, and the essence of his prophecies laid in his actions. This is important to note.
There are also times when one uttered prophecies unwittingly, and some may say unwillingly since it went against the claimer's interest. Consider the cases of Balaam (Num 22) and King Saul (1 Sam 19). In the NT we see the case of unrighteous Caiaphas proclaiming the Jesus must die for the nation (Jn 11:51).
To get more specific to your question we must explore the NT scriptures. Specifically the spontaneous utterances people proclaimed which served God's immediate purpose of proclaiming His Messiah. And there's the Words of the Messiah Himself. And lastly, the Word Jesus commissioned His Apostles and future followers to proclaim.
The Spirit of God spoke through Zacharias upon the birth of John the Baptist:
Luk 1:67 And his father Zacharias was filled with the Holy Ghost, and
prophesied, saying, Luk 1:68 Blessed be the Lord, the God of Israel;
For he hath visited and wrought redemption for his people, Luk 1:69
And hath raised up a horn of salvation for us In the house of his
No doubt this was a spontaneous work of the Lord. But the far most important prophecies where through Jesus Christ, in which they were in both Word and deed. Specifically Jesus finished work on the cross fulfilling the offices of prophet, high priest, and King, which were only seen in types and shadows in the OT.
Heb 1:1 God, having of old time spoken unto the fathers in the
prophets by divers portions and in divers manners, Heb 1:2 hath at
the end of these days spoken unto us in his Son, whom he appointed
heir of all things, through whom also he made the worlds.
The book of Hebrews makes clear that Jesus the Messiah is God's true and final revelation to man. But we must not consider Jesus' ascent into heaven the end of prophecy. The same Spirit that dwelt in Christ, without measure (Jn 3:24), dwells in everyone who calls upon His name. Which implies that everyone who proclaims the scriptures in reference to Jesus current reign as Lord of all prophesies. If we look back to the Hebrew scriptures this truth is a fulfillment of scripture.
Num 11:29 And Moses said unto him, Art thou jealous for my sake?
would God that all the LORD'S people were prophets, that the LORD
would put his spirit upon them!
There is much diversity in the subject of prophesy. The OT major and minor prophets provided much in the area of foretelling. But the NT provides much in the way of forthtelling. That is, the present reality is here (the Messiah) and He fulfills all of what the Hebrew scriptures were all about (Lk 24:45). In 1 Cor 14, Paul placed heavy emphasis on building up the Body of Christ through the preaching of the gospel. This was at a time when the Hebrew scriptures served as their Living Word. Since believers today are blessed with the canon of scripture, we must proclaim, or better yet prophecy, all that Jesus accomplished.