No difference at all. In this case $query is an object and it will internally set the filter, but it also returns itself, to provide chaining:
$query->where( 'id','=',1 )->where( 'name','=', 'antonio' );
So those two are exactly the same.
$query = $query->where( 'id','=',1 );
$query->where( 'id','=',1 );