Yes the church is the catholic church.
And if I'm not mistaken, the catholic church was created by Peter, who many catholics point to as the first Pope.
Catholic Church was created by Jesus Christ. Peter was given special duty to lead and care his flock. Jesus give this job personally to Peter after the resurrection. You can read that in John 21:15-17
21:15 Then when they had finished breakfast, Jesus said to Simon Peter, "Simon, son of John, do you love me more than these do?" He replied, "Yes, Lord, you know I love you." Jesus told him, "Feed my lambs."
21:16 Jesus said a second time, "Simon, son of John, do you love me?" He replied, "Yes, Lord, you know I love you." Jesus told him, "Shepherd my sheep." 21:17 Jesus said a third time, "Simon, son of John, do you love me?" Peter was distressed that Jesus asked him a third time, "Do you love me?" and said, "Lord, you know everything. You know that I love you." Jesus replied, "Feed my sheep.
This is of course if you are referring to "the church" as the catholic church and not the body of christ church, which encompasses every christian religion.
There is some confusion there.
I am sorry I confused you. To put it straight, the other Christian sects are not in full communion with the body of christ church. To put it bluntly, they're heretic and has broken away from the body of christ church which you call the catholic church.
When one broken away from the body of christ, they don't share the same belief anymore. That's why they have things such election of woman priest or the subject of this topic.