This root-word can be used for one of two things: a “messenger” (of equal representation of its sender),  and “skilled task”. These tasks are always charged from a categorically higher authority. Terms like “angel”, found in most translations, are but a semantically assimilated rendition from the Greek translation of this term; angelos.
The following are cases where the root is used to refer to physical messengers. Here, the messenger (of God) that brought the Israelites out of Egypt, is none other than Moses: 
וַנִּצְעַק אֶל יְהֹוָה וַיִּשְׁמַע קֹלֵנוּ וַיִּשְׁלַח מַלְאָךְ וַיֹּצִאֵנוּ מִמִּצְרָיִם
“And we cried out to The Lord, and he heard our voice, and he sent a messenger, and he took us out of Egypt…” (Num. 20:16).
The messengers of Balak bear the authority of the word of their king:
וַיִּשְׁלַח מַלְאָכִים אֶל בִּלְעָם בֶּן בְּעוֹר פְּתוֹרָה
And he (Balak) sent messengers to Balaam son of Be’or, towards Pethor…” (ibid 22:5).
וַיִּשְׁלַח מַלְאַךְ יְהוָה אֶת קְצֵה הַמִּשְׁעֶנֶת אֲשֶׁר בְּיָדוֹ וַיִּגַּע בַּבָּשָׂר וּבַמַּצּוֹת וַתַּעַל הָאֵשׁ מִן הַצּוּר וַתֹּאכַל אֶת-הַבָּשָׂר וְאֶת הַמַּצּוֹת וּמַלְאַךְ יְהוָה הָלַךְ מֵעֵינָיו
“The messenger of The Lord sent the tip of the staff that was in his hand, and he touched the meat and unleavened cakes, and the fire came up from the rock and consumed the meat and unleavened cakes, and the messenger of the Lord went [away] from his eyes” (Jud. 6:21).
וַתִּשְׁלַח אִיזֶבֶל מַלְאָךְ אֶל אֵלִיָּהוּ לֵאמֹר כֹּה יַעֲשׂוּן אֱלֹהִים וְכֹה יוֹסִפוּן כִּי כָעֵת מָחָר אָשִׂים אֶת נַפְשְׁךָ כְּנֶפֶשׁ אַחַד מֵהֶם
“And Isabelle sent a messenger to Elijah, saying: so shall God do and so shall he continue [to do], for tomorrow I will place your soul as the souls of one of them” (1 Kings 19:2).
There are instances where the term may refer to metaphysical or cosmic tools of God, but I will save myself the trouble of dealing with those verses, as they are not essential to understand the root-word of discussion. Elsewhere, the same root is used to describe tasks of unique instruction and training. I conjecture that the root LAK is used here, as these tasks were usually done by the appointment of those skilled in them.
Individuals of unique caliber were appointed to build the Tabernacle:
מִלֵּא אֹתָם חָכְמַת לֵב לַעֲשׂוֹת כָּל מְלֶאכֶת חָרָשׁ וְחֹשֵׁב וְרֹקֵם בַּתְּכֵלֶת וּבָאַרְגָּמָן בְּתוֹלַעַת הַשָּׁנִי וּבַשֵּׁשׁ וְאֹרֵג עֹשֵׂי כָּל מְלָאכָה וְחֹשְׁבֵי מַחֲשָׁבֹת
“He has filled them with the skill to execute all types of engraving work, and embroidering, and the making of variegated cloth of royal blue, and of violet, and of scarlet yarn and of fine linen, and as weavers, as performers of every work and reckoners of designs.” (Ex. 35:35)
Here, melakha is also used to refer to a skilled craft:
וָאֵרֵד בֵּית הַיּוֹצֵר וְהִנֵּה הוּא עֹשֶׂה מְלָאכָה עַל הָאָבְנָיִם
“Then I went down to the artisan’s house, and there he was, crafting something on the stone” (Jer. 18:3).
King Solomon did not look to see if Jeroboam did ordinary “work”, but rather, to see if he carried out professional tasks:
וְהָאִישׁ יָרָבְעָם גִּבּוֹר חָיִל וַיַּרְא שְׁלֹמֹה אֶת הַנַּעַר כִּי עֹשֵׂה מְלָאכָה הוּא וַיַּפְקֵד אֹתוֹ לְכָל סֵבֶל בֵּית יוֹסֵף
“And the man Jeroboam was a mighty warrior, and Solomon saw that the lad was industrious, and he appointed him over all the forced labor of the house of Joseph” (1 Kings 11:28).
As in the case of King Solomon, regarding the “tasks” that Joseph performed, Potiphar specifically appointed him to perform them:
וַיְהִי כְּהַיּוֹם הַזֶּה וַיָּבֹא הַבַּיְתָה לַעֲשׂוֹת מְלַאכְתּוֹ וְאֵין אִישׁ מֵאַנְשֵׁי הַבַּיִת שָׁם בַּבָּיִת
“Now it happened one day that he went into the house to perform his tasks, and none of the men of the household were there; in the house” (Gen. 39:11).
וַיִּמְצָא יוֹסֵף חֵן בְּעֵינָיו וַיְשָׁרֶת אֹתוֹ וַיַּפְקִדֵהוּ עַל בֵּיתוֹ וְכָל יֶשׁ לוֹ נָתַן בְּיָדוֹ
“And Joseph found grace in his eyes, and he served him, and he appointed him over his house, and all that was his, he gave over to his dominion” (Ibid v. 4).
Upon the rebuilding of the second Temple, which involved serious craftsmanship, the verse relates:
גַּם בָּעֵת הַהִיא אָמַרְתִּי לָעָם אִישׁ וְנַעֲרוֹ יָלִינוּ בְּתוֹךְ יְרוּשָׁלִָם וְהָיוּ לָנוּ הַלַּיְלָה מִשְׁמָר וְהַיּוֹם מְלָאכָה
“Also at that time, I said to the nation; ‘each man and his lad shall sleep within Jerusalem, and the night shall be for us a watch [duty], and the day for labor’” (Neḥ 4:16).
וְיוֹם הַשְּׁבִיעִי שַׁבָּת לַיהֹוָה אֱלֹהֶיךָ לֹא תַעֲשֶׂה כָל מְלָאכָה אַתָּה וּבִנְךָ וּבִתֶּךָ וְעַבְדְּךָ וַאֲמָתֶךָ וְשׁוֹרְךָ וַחֲמֹרְךָ וְכָל בְּהֶמְתֶּךָ וְגֵרְךָ אֲשֶׁר בִּשְׁעָרֶיךָ לְמַעַן יָנוּחַ עַבְדְּךָ וַאֲמָתְךָ כָּמוֹךָ
“And on the seventh day, it is a Sabbath for The Lord your God. Do not perform any tasks; you, and your son, and your daughter, and your servant, and your maidservant, and your ox, and your ass, and all your animals, and your stranger that is in your gates, so that your servant and maidservant shall rest like you” (Deu. 5:14).
Evidently, the Tora is not instructing the Israelites to abstain from any kind of “work”. The tasks that are restricted are of a specific, skilled nature. Thus, the Tora provides a day of asylum from the professional tasks occupying the minds and energy of the people throughout the week. 
 The Talmudic canon “a man’s messenger is like himself” is not without scriptural basis. Gen. 19:13 relates that the “messengers” visiting Lot were to destroy his region. Later (v. 24), the texts relate that The Lord rained “sulfur and flames” onto the region. See the comments of R. Samuel b. Meir (commentary to Genesis 18:1), where he concurs with this theory.
 Malakh is thus synonymous with the Arabic rasul; the Quran’s title for Muhammad: a messenger (of Allah). Indeed, R. Saadia Gaon and Maimonides refer to Moses as Rasul Allah. See http://personal.colby.edu/~dfreiden/Freidenreich_Use_of_Islamic_sources.pdf, P.362.
 The statutes discussing halting from these activities on the Sabbath and festivals categorize it as “all” melakha; implying categorical restriction. This lead the Sages (Shabbat 49b) to define this term in light of the juxtaposition of melakha (Exo. 21) used to describe the building of the Tabernacle, and the restricted activities on the Sabbath.