Short answer: Biblically, no; practically, perhaps.
Long answer: The public ministry of the Word is sometimes divided into preaching and teaching, with various ways to distinguish between them. Adams (Adams 1982, 5‑6), Zuck (Zuck 1998, 39‑40), and Dodd (Dodd 1980, 7‑35) distinguish between preaching (κηρύσσω and eὐαγγελίζω) and teaching (διδάσκω) in terms of the audience. In this view, preaching is evangelistic activity among unbelievers while teaching is the work of moral or ethical instruction among believers. For Dodd, in particular, the distinction is related to the content, rather than the act of preaching itself (Dodd 1980, 7‑8). Singley (Singley, III 2008, 45‑46) and Prime and Begg (Prime and Begg 2004, 125; cf. Anderson 2006, 93‑94) distinguish between preaching and teaching in terms of intent or goal. In this conception, teaching has as its goal the communication of knowledge whereas preaching has as its goal the movement of the will and emotions to respond to the truth communicated.
While these distinctions may have practical value, it seems doubtful that they can be rigidly sustained from Scripture since the various words used do not fit neatly into the categories of preaching or teaching. Frequently, the words preaching and teaching themselves are not used precisely. For instance, the public ministry of the word is described by using preaching (κηρύσσω or εὐαγγλίζω) and teaching (διδάσκω) alongside each other (Matt 4:23; 9:35; 11:1; Acts 5:42, 13:35, 28:31). The context of these passages do not lend themselves easily to a distinction between preaching and teaching, whether by audience or content, or by goal or intent. They seem to describe the public ministry of the word as a whole rather than as distinct parts. Teaching (διδάσκω) is used for gospel preaching to unbelievers in Acts 4:2, 5:21, and 20:20, and it is used for teaching believers in passages such as Acts 11:26, 18:11, and 1 Tim 4:11. Preaching (κηρύσσω or εὐαγγλίζω) is used for evangelistic work among unbelievers in passages such as Acts 8:4 and 25, and 1 Cor 1:23 and 2:4, and it is used for teaching believers in 2 Tim 4:2. In addition, there are passages in which the spiritual state of the audience for either preaching or teaching is not clearly distinguished.
To use a specific example, in Acts 20:17-35, Paul recounts his entire ministry among the Ephesians “from the day he set foot in Asia” (v. 18) with various terms. He uses proclaiming (ἀναγγέλλω), teaching (διδάσκω), and solemnly testifying (διαμαρτύρομαι) to describe the gospel proclamation of “repentance toward God and faith in our Lord Jesus Christ” (vv. 20-21). He further describes his ministry among them as “preaching (κηρύσσω) the kingdom” (v. 25), “declaring (ἀναγγέλλω) the whole purpose of God” (v. 27), and “admonishing (νουθετέω) each one with tears” (v. 31). Here, there seems to be no consistent division between gospel preaching and ethical teaching. The various terms describe the entire ministry of Paul.
In Thessalonica and Athens, Paul reasons (διαλέγομαι) with unbelievers in the synagogue (Acts 17:2, 17), which is the same word used to describe his ministry with believers at Troas (Acts 20:7, 9). This same word (διαλέγομαι) is used for ministry both with believers and unbelievers in Ephesus (Acts 19:8-9). In Athens at Mars’ Hill, Paul “was preaching (εὐαγγλίζω) Jesus and the resurrection” which led the hearers there to inquire more about “this new teaching (διδαχή) … which [he was] proclaiming (λαλέω)” (Acts 17:18-19). Here, the teaching was being preached. In 2 Tim 4:2, κηρύσσω, a key word for preaching to unbelievers, is used for preaching to believers.
In light of these instances in which the same words are used to describe ministry both to believers and unbelievers, and seeing that no clear distinction is consistently apparent between goal or intent of preaching, the distinction between preaching and teaching seems to fade into the background. The full picture of the ministry of the Word is better seen in the totality of the words used to describe it. Greidanus helpfully says, “Preaching can be seen as an activity with many facets—facets which are highlighted by such New Testament words as proclaiming, announcing good news, witnessing, teaching, prophesying, and exhorting” (Greidanus 1988, 7).
The distinction in content or emphasis between the ministry of the Word to unbelievers and believers is a valid one since the two groups often need to hear different messages. Likewise, the distinction between teaching as informing the hearer of truth and preaching as appealing to the will and emotions to respond to the truth is helpful. Yet these distinctions seem borne more out of practicality than out of the words Scripture uses for the preaching task. Again, Greidanus is helpful: “Although one facet or another may certainly be accentuated to match the text and the contemporary audience, preaching cannot be reduced to only one of its many facets” (Greidanus 1988, 7).
A distinction between preaching and teaching may be useful when considering the various speaking opportunities in the church. There are occasions where the particular forum will involve more teaching (communicating truth) than preaching (persuading). There are also occasions where the audience will include unbelievers in needed of gospel proclamation, and other times where it will be mostly believers in need of ethical and moral instruction. The wise pastor will be sensitive to these occasions and adjust both his content and his intent accordingly.