Is the Church an Organization? A Look at Matthew 16:18

When Peter told Jesus He was the Son of the living God, Jesus responded, "You are Peter (small rock), and upon this rock (big rock) I will build my church; and the gates of hell shall not prevail against it." Jesus was not referring to an organization or institution of man under the State made of brick and stone, but to those "called out ones" who came under that foundation to gather in His name as He is the Son of the living God. What is different than our model today?

Scriptures: Matt 16:18, Acts 7:48-51, Acts 17:24, John 2:19, Matt 26:61, Acts 2:46, Acts 5:24, 1 Cor 3:16, 2 Cor 6:16, Eph 2:21, 1 Pet 5:2, Hebrews 5:12, 2 Tim 3:7, Hebrews 8:2, Hebrews 10:25