So do you share Peters definition ?
Most definitely.
Is it the only definition ?
There are 'other descriptions' of the church, but none which is at variance with that of Peter.
Are there different "types" of "church" ?
No ... there is only one church ... bought with the blood of Jesus Christ, Himself ... wrought by the grace of God ... and batized by His Spirit.1 Corinthians 12:12 For as the body is one, and hath many members, and all the members of that one body, being many, are one body: so also is Christ.
13 For by one Spirit are we all baptized into one body, whether we be Jews or Gentiles, whether we be bond or free; and have been all made to drink into one Spirit.
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1 Corinthians 12:27 Now ye are the body of Christ, and members in particular.
28 And God hath set some in the church, first apostles, secondarily prophets, thirdly teachers, after that miracles, then gifts of healings, helps, governments, diversities of tongues.
29 Are all apostles? are all prophets? are all teachers? are all workers of miracles?
30 Have all the gifts of healing? do all speak with tongues? do all interpret?
31 But covet earnestly the best gifts: and yet shew I unto you a more excellent way.
Was this Paul's opinion, or was he expecting that those in Corinth would recognize his authority as a teacher?
Were those in Corinth free as Christians to reject Paul and decide all matters for themselves? Is that the model of ecclesial authority one finds inherent in the New Testament?
SD
So you don't believe that Christ founded a Church in Matthew 16:18? You see "church" as simply a body of believers? Is that correct?