Why do the gospels differ in showing how Jesus called his first
disciples? The book of John describes the encounter differently from the
other gospel books.

I am assuming that you are referring to John 1:35-42, which is
obviously significantly different from, for example Mark 1:14-20. I have
always assumed that when Jesus formally called the first disciples to join
him permanently in his ministry in Mark 1:14-20, that this was not the
first time he had met Peter, Andrew, James and John. The very first time
I read Mark 1, I thought perhaps that this was the first time they had
ever met Jesus, but the more I thought about it, the way they responded to
the call seemed to me to represent men who knew Jesus well, and were
already prepared to consider following him. This was not the first time
they had met him.

Having reached that conclusion, it then becomes easy to see
where John 1:35-42 fits in. This is the account of the first time these
fishermen actually met Jesus. They spent some time with him at his house,
witnessing his miraculous understanding of the heart of Nathanael, hearing
him speak of his ministry and so forth. Several weeks or perhaps even
several months later, when Jesus came to their home town to call them into
the full-time work of following him, they were well prepared by their
previous knowledge of Jesus, as described in John chapter one. When Jesus
called them to follow him, he was asking men who knew him well and had at
least some idea of what they were getting into when they left their nets
and followed him.

By this description, John 1 is the first time the disciples
met Jesus, but the “calling of the first disciples” would be recorded in
Mark 1 and Matthew 4:18-21.
John Oakes