This post discusses latreuo, the Romans 12:1 semantic subdomain, and a more delineated understanding and practice (part B)
Most Christians have not understood the distinction between horizontal and vertical, and they sometimes gush forth about “such great worship this morning” when there has been no vertical component. Not that there must be a vertical component in every gathering, but when the nature and purpose of any activity is clearly understood, its practice will be enhanced.
When I first read Karen Jobes’s fine word study on worship words about six months ago, it gave me a new lease on thought-life in this area, so it’s probably bad form to begin a treatment of her work with a criticism. I think this will really amount to a clarification, not a criticism, because there is good reason for her to have done what she did in writing for English Bible readers.
→ Jobes takes as her jumping-off-point all the words in the semantic domain for the English word “worship” rather than beginning with Greek words and concepts. In other words, she takes as her sample a complete list of the English-Bible instances of “worship” and investigates what’s beneath them.
Her premise is fine, given that she’s explaining things primarily for English readers. But I think the water actually gets a little muddy right off the bat for those trying to get to the bottom of all this.
If our goal is to understand what the referents are when we see “worship” in Bibles, OK. If our goal, rather, is to understand how the earliest Christians thought about and practiced vertical worship, we might want to exclude a few things from Jobes’s study, or at least treat them separately. You make the call for yourself. In the end, I think you’ll see the differentiation, regardless.
Here, I’ll start with the very two words that could throw the unsuspecting reader off track:
Latreuō and leitourgeō share a very specific sense that distinguishes them from the other Greek verbs for worship that have a wider semantic range. In the New Testament latreuō is used to designate duties performed in a religious vocation. Forms . . . are used . . . to refer to the temple service of Anna (Luke 2:37) and the altar work of the Old Testament priests (Heb. 8:5). 
The observation that latreuō in the NT refers to OT priests is crucial before we notice another text—Romans 12:1—and in it, an often-quoted NT instance of a noun form of latreuō, one of the words captioned above:
I appeal to you therefore, brothers, by the mercies of God, to present your bodies as a living sacrifice, holy and acceptable to God, which is your spiritual worship.*
* “Worship” (here in the ESV) is latreian in the original.
It is not within my intended scope in this post to treat Romans 12:1-2 contextually, and I’m not currently qualified to do that. I do know enough about Romans to know that Israel’s history and theology are involved, so it makes perfect sense to read latreuō in Romans as a reference to the Levitical priesthood. The priestly “religious vocation” (as Jobes termed it) of course gets a facelift under the New Covenant, and a morphed understanding seems to be what Paul is advocating. Here is Jobes again:
Paul is drawing a close parallel between Israel’s priests and the priesthood of all Christian believers. The priests of Israel offered sacrifices of dead animal flesh. . . . What sacrifice, if any, is logikén—that is, reasonable or appropriate—for the corresponding Christian priesthood of believers to offer? According to Romans 12:1, . . . his or her own living human flesh. . . . 
Paul, then, is speaking of what Hebrew priests did in their vocational life and then is putting the offering of the Christian’s body into that frame.
Many modern Christians become confused here. Based largely on Romans 12:1-2, they make Paul out to be saying that vertical worship is superfluous and that everything is summed up in so-called whole-life worship. The logical inference, then, would be that Paul was negating, for instance, humble prayer he would have known from the Psalms, the worship of Isaiah, or the unrestrained praise of Miriam. No, Paul was not negating vertical worship. He wasn’t even dealing with it in Romans 12.
Paradoxically, many of the same Christians seem to hold in mind a relatively consistent grouping of mostly vertical activities, placing them under the mental heading “worship.” It is an interpretive mistake to make the word latreian in Romans 12 refer directly to things in that grouping.
Summing up, for today
A single discussion might include such diverse English terms as worship and service and OT priests and honor and glorification and praise and religious ritual. One can maintain a clearer head if he will differentiate the meanings of the original Greek words. Whether you want to place latreuō in your worship category or not, it is undeniable that latreuō is referring to a different set of things than those referred to by some of the other words translated “worship.”
The overarching point is this: we mustn’t indiscriminately intermingle all the times we see “worship” in the Bible. It may not be assumed that each refers to the same thing; however, they may all be reasonably included in the same discussion, if one takes care.
 In these posts, I will use transliterated English spellings of Greek words, although Jobes uses Greek.
 Among other salient aspects here above are the words “In the New Testament.” While we Christians might simply pass over those words thoughtlessly, I would point out that it is often important to notice how a word is used in scripture as well as how it is, or isn’t, used in secular literature and in non-canonical sacred writings.
 Karen Jobes, “Distinguishing the Meaning of Greek Verbs in the Semantic Domain for Worship,” in Moisés Silva, Biblical Words and Their Meaning: An Introduction to Lexical Semantics (1994), 203.
 Ibid., 204