I have seen both of these syntaxes for adding constraints to an existing Fluent/Eloquent $query (such as when appending a constraint based on a conditional):
$query = $query->where( 'id','=',1 );
and
$query->where( 'id','=',1 );
Is there any practical difference between them?
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 );