What does missionary and mission mean?
A missionary is a member of a religious group sent to a particular area to do proselytizing or to do some services, such as education, learning, social and charitable services, medical care, and economic development. The word MISSIONARY has been known since 1598 when the Jesuits sent their members (monks) abroad and derives from the Latin missionem (subst. Missio), which means "act of sending" or mittere, which means "to send". This word was and is used in its biblical light, in the Latin translation of the Bible, where Jesus Christ uses it when he sends his disciples to preach / preach the gospel in His name. 
Missionaries are a group of people sent to a foreign country for a specific purpose; it is a delegation, and their action is supported by the church to convert and bring the so-called "unbelievers" on the "right path."
Mission is the action of spreading Christianity in countries with another dominant religion, from the Latin missio / missionis = sending, assignment, or vocation / calling of a religious organization, especially Christian, to go into the world (in other countries) as to spread their faith. 
Speaking of mission, John Stott and Christopher Wright said, “The word mission cannot be used correctly to cover everything God does in the world. In His providence and grace, He is truly active in all people and in all societies, whether they recognize Him or not. But this is not His mission. "Mission" refers to people redeemed by Him who are sent to do what He has given them. "
In the Word of Truth of May 2019 we find written the following : “The well-known missionary David Bosch proposes a distinction between the terms mission (singular) and missions (plural), the first referring to missio Dei, which is: a. His self-revelation God as the One who loves the world He created, b. God's involvement in and with the world, and c. The nature of God's activity — embracing both the Church and the world in which the Church has the privilege of actively participating: we are workers with God ... ”(1 Cor. 3.9a - Revised Dumitru Cornilescu Edition, 2019). Missio Dei is the good news that God is a God to men. The term mission refers to particular forms - related to specific times, geographical locations or needs - of participation in missio Dei. ”
In the definition of the missionary appeared another word that must be explained, it is the word proselytism which is the act of trying to convert people to another religion or another opinion. Proselytism derives from the Greek προσήλυτος (prosélytos, "newcomer" consisting of the prefix προσ- (pros-, "to") and the verb ἔρχομαι (érchomai, "I come"). proselytizing was given to a non-Christian / pagan who considered conversion to Judaism. 
I consider it good to also explain the meaning and origin of the word APOSTLE , because we will continue to use it, related to the work of the apostles and Christians as followers of Jesus Christ. An apostle, in its most literal sense, is an emissary, from the Greek ἀπόστολος (apostle), meaning "one who is sent," from the verb ἀποστέλλειν (apostéllein), "to be sent." The purpose of sending is to send a message, so the alternative translation of "messenger" is also used; another translation being "ambassador" and "special messenger," "the apostolic adjective is used by a number of Christian churches that follow the teaching of the apostles." 
 Wikipedia: Missionary, https://en.wikipedia.org/wiki/Missionary
 “Wikipedia: Mission”, Lexico.com, https://www.lexico.com/definition/mission
 Christopher J. H Wright and John R. W Stott, Christian Mission in the Modern World. (Downers Grove, IL: Inter-Varsity Press, 2016), 19.
 Daniel Purdel, The Word of Truth, Bulletin of Pentecostal Christian Worship, Series II, Year XXIX, No. 5 (Bucharest, May 2019), 3
 David J. Bosch, Transforming mission: paradigm shifts in theology of mission, Twentieth anniversary ed, American Society of Missiology series, no. 16 (Maryknoll, N.Y .: Orbis Books, 2011), 10.
 “Wikipedia: Proselytism”, https://en.wikipedia.org/wiki/Proselytism
 Green, The Interlinear Bible: Hebrew-Greek-English: with Strong's concordance numbers above each word, (Peabody MA, Hendrickson Publishers, 1986), 872.
 "Wikipedia: Apostle", https://en.wikipedia.org/wiki/Apostle