Andrew and John went home with Jesus and visited and listened for a whole afternoon. Later Jesus was preaching by the seashore, and he called these four to come and follow him: John and his brother James, Andrew and his brother Peter. Jesus said to them and to Nathaniel, and Philip, "Come follow me." He also called Matthew who was a tax collector with the same message.
This was a more intense call. It was no longer just an invitation to see where he lived or what he ate, but an invitation of involvement: Come see what I preach, and who I touch, and where I go. Now it became "Come do what I do."
That is the invitation he wanted those disciples to accept, and it is still the invitation he extends to his listeners today. To those who hear his call, the invitation is not just one of investigation or casual interest, but participation in the mission of spreading the word and love of God.
Read Matthew 4, Mark 1, John 1, and Luke 4 and 5 for a fuller explanation of the call of the disciples.