mcraz said:

You are a bit wrong ;)

First off to answer OP question:

$model->relation   // dynamic property -> lazy loads the relation, returns Collection
$model->relation() // returns Relation Object, thus operates on the relation query, nothing is loaded now

$model->relation()->first(); // runs as relation query ->first(), doesn't load the relation at all
// first here is a method on the Query Builder

$model->relation->first(); // loads the related models and fetches first from the collection
//  while this time first is the method on the Collection

// You can also lazy load the relation like this:
$model->load('relationName');

Now about the eager loading:

$posts = User::find(1)->posts(); // no queries at all for the posts

$posts = User::find(1)->posts; // lazy loads posts (2 queries)
// the same as
$posts = User::with('posts')->find(1)->posts; // 2 queries as well

$posts = User::find(1)->with('posts')->posts(); // ERROR, no 'posts' method on the query builder

Eager loading is supposed to avoid n+1 issue, which occurs when you do this:

$users = User::take(10)->get();

foreach ($users as $user) { 
  $user->posts; // this runs query for each user = 11 queries
}

// eager loading:
$users = User::with('posts')->take(10)->get(); // 2 queries

// or lazy loading on the Collection, doing the same as above
$users = User::take(10)->get();
$users->load('posts');

// then in that foreach loop no queries will be run, 
// because posts were already matched to the users and are accessible on $user->posts;

So no need to eager load anything if you work with single parent (User in the example).