> order.line_items != LineItem.where(:order_id => order.id)

Let me rephrase Robert's words.
The key difference here is, that LineItem.where(:order_id => order.id)
doesn't fire the sql and returns ActiveRecord::Relation object.
While the order.line_items runs SQL and returns the Array of records.
The purpose of it is that u can change the resulting SQL and do the
method chaining.

Try next:
line_items_by_order_id = LineItem.where(:order_id => order.id) # =>
object of ActiveRecord::Relation class
ordered_line_items_by_order_id = LineItem.where(:order_id =>
order.id).order(:updated_at) # => object of ActiveRecord::Relation
class
ordered_line_items_by_order_id_with_positive_price =
LineItem.where(:order_id =>
order.id).order(:updated_at).where("line_items.price > ?", 20) # =>
object of ActiveRecord::Relation class
# ... and so on
# where
order.line_items # returns [LineItem, LineItem ...] array

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