"Preaching" and "teaching" are terms the NT often uses interchangeably. Depending on the context, they may be regarded as synonyms. On occasion, a distinction between the terms may give the reader/interpreter a nuanced appreciation for the author's meaning, just as a combination of them in one context may supply a fullness of description.
To understand Paul's intent in 1Tim.2:12, one could begin by grasping the purpose (or combined purpose) for writing the letter. In this vein, an awareness of who Timothy is, where he ministers and how he came to occupy his position, with the possible motivations Paul has for writing--all items usually gleaned from the letter itself, as well as from other NT documents--such will surely prove valuable for hermeneutics, even at the scale of a single verse. It's always helpful to grasp widely Paul's whole corpus, when studying any lesser part of it, for then one has both access to the author's sweep of interests and a general chronological sequence of putting his various concerns into print.
Timothy is leading the church in Ephesus, where Paul was most recently the chief minister (compare 1Tim.1:2 and Act.20:1). The counsel Timothy gets from the apostle is meant to aid him in his role, and to guide him and other church leadership (either already present or which Timothy will now have a vital part to play in shaping) as they shepherd the church in worship, and its members in life in the "kingdom subculture" that is the church in the world.
In ch.2, Paul has just completed a section wherein he encouraged the church at prayer, both in the general and corporate interest; and also speaking particularly to men and to women, as their lives affect the church at prayer. He addresses both sexes, noting what may be called "stereotypical" sins or tendencies to each that left unchecked or unguarded will harm or distract the church at prayer.
Arriving at v12, Paul yet feels prompted to insist that whatever permissions are found in the affirmations he has just noted, it does not affect order in the church in its primary functions: worship and discipline. Whatever encouragements to participation in prayer enjoyed by women in the church, the rule of their silence for the sake of the subjects "teaching" and "authority" has no diminution.
It is helpful to compare these instructions to those that were sent to the Corinthian church (not long prior, on the timeline I favor). His counsel to that church (N.B. chs. 11-14) still pretty fresh in his mind, addressed challenges to order in the church some of which appears to have been predicated on the notion: "If I have a Spirit-given gift, then this fact means I should be using it whenever it strikes me as fitting." Apparently, one area this manifested itself in Corinth (though in 11:2 he indicates the leaders there were managing to hold the line here) was that women with the prophetic gift were bucking the apostolic imposition of church order (and see 11:16).
As he wraps that whole 4ch section, Paul summarizes key points of the apostolic church order, including 14:34, instructing women to be silent in the churches. This cannot mean that women never had any voice as Christians! Nor that they never taught anyone, for there is indisputable respect given to Priscilla for teaching, Act.18:26. No, but Paul is concerned in that whole section for order in the church, i.e. its gathering for worship, its liturgy both of the word (matters of proclamation including prophecy) and of sacrament (note the lengthy discussion of Lord's Supper propriety). Thus, we find consistency between Paul's instruction in two letters, one where the church order was threatened, the other where a similar threat should be preempted.
1Cor.14:35 should make it obvious that learning is natural and vital to Christians; and learning's counterpart, teaching, has always been understood to be an important element of Christian worship. A woman's question is not unimportant, as if she was unimportant. I don't think Paul's instruction assumes that it was OK for a MAN to interrupt and ask a question in the midst of worship; just above this portion, Paul adamantly states it is unseemly for anyone to speak out of turn in worship! More positively, we might want to inquire: what spiritual reality goes unappreciated or ignored when the "golden silence" of God's women is repudiated? He commanded it, so it must be for our benefit; but... certain elements in the church prefer something else before his command.
Returning to 1Tim.2:12, unless we aim to expand as far as possible the limit that God, through Paul, places on that silence--it seems abundantly clear to me that we should constrain the limit to only include the church's worship and government--which two places are the only ones where a sex-specific order accompanies the descriptions found in the Bible. I fear it is adding to the Lord's instructions, even if to "safeguard the limit" (doesn't that sound familiar?!). I'm fine granting anyone his further conviction as to increasing the limitation, 1) so long as it has some plausible scriptural support; and 2) so long as we can live-and-let-live, allowing the other side accepts the principle of biblical authority.
"To teach" in 1Tim.2:12 is expressive of the word-based essence of Christian worship, in which teaching the content of the Bible, or explaining the mind of God to instruct his followers is central to the purpose of the gathered congregation. The language "have authority" in the same verse is expressive of the essence of government, in this case church-government under Christ's kingship. "To teach" cannot mean women never teach at all in or for the church, if for no other reason than Paul would directly contradict himself in Tit.2:4.
Eph.4:11 identifies as the ordinary successor office to the apostle's, the "pastor-teacher." Note, he doesn't name this calling "preacher," even though that designation is fairly standard. The specific nomenclature is various because, as our books of church order are wont to express the fact: the office is multifaceted. Preacher, minister, teacher, overseer, shepherd, etc.
Hopefully this is helpful.
