Missions and missionary are not listed in the scriptures, so we don't have a Biblical definition for these words, but we do have examples we can use to help us understand.
Many look at Acts 1:8, as a definition of missions, and it can be, but I believe it is more. One reason is because when Jesus said this it was not just for a few, but for all who were listening, and for us today.
This to me is a calling for all to be in ministry, and they will minister (preach the Gospel) in different places – some at home, some in other places, some in other cultures, some in other lands – establishing the Kingdom of God. And when you connect this verse with others Jesus said about preaching the Gospel and making disciples, it is our calling as a believer. This becomes our "mission", our assignment if you will, – both individually and corporately.
One way to separate the parts of our "mission" is by looking at it as having two parts – evangelism (ministry within one's own culture, or in a similar one) and missions (cross-cultural ministry). We can see this example in the scriptures. The disciples in acts began their ministry within their own culture - evangelism. After persecution began, it forced them to take the next step. In Acts 8:4-5, we see Phillip heading off to a city in Samaria. This was in a similar culture, but was not his own – still evangelism. Then in Acts 13:1-4, we find the first instance of ministry being sent out by the church – missionaries going to other cultures.
So to me, "Missions" means the sending of called ones to do ministry (our "mission") in a culture which is not their own. Evangelism is ministry (our "mission") within one's own, or in a similar, culture. Missions does not have a definition based on location, but is based on culture.