What is the difference between presenting costs by their nature and by their function on the P&L?

There are two main types of profit & loss statement:

But regardless of how the P&L is presented, the operating profit is still the same!

Presentation of costs by their function
This is based on an analytical approach to the company, which classifies costs by major functions within the company

Personnel costs, for example, are broken down in each of these four functions (or three when sales & marketing costs and administrative costs are merged into one item), depending on whether the employee works in production, sales, R&D or administration. Similarly, the depreciation of a tangible fixed asset will be put under production costs if it is a machine, under sales & marketing costs if it is a salesperson's car, under R&D costs if it is laboratory equipment and under administrative costs if it is the accounting department's computers.

Presentation of costs by their nature
This is the traditional presentation in France and many continental European countries. Obviously, in this approach, operating income, as in the previous case, is the difference between sales and the cost of these sales.
European practice calls for booking costs when they are contracted, not when they are consumed.
If the P&L shows, on the one hand, all purchases made during the year and, on the other hand, all invoices sent to clients, then we're comparing apples and oranges. After all, a company can stock some of the purchases it made during the year. This is not value destruction, but, rather, the constitution of an asset that is no doubt temporary, but quite real at a given moment.
Meanwhile, it is possible that some of the company's finished products will not be sold during the year and, yet, the costs pertaining to these products appear on the P&L.
So to avoid comparing apples and oranges, we have to make some adjustments, i.e.

Booking costs by their function starts with revenues and then reconstitutes the costs of these goods or services sold, in order to reach the operating profit. Booking costs by their nature starts from operating purchases and then adjusts them for changes in inventories of raw materials and finished products, in order to reach the operating profit, through subtraction from revenues (1).

A new presentation?
A third way of presenting the P&L has emerged, in particular in France and the US. It looks like a presentation by function, except that it does not split up depreciation between various cost items but isolates it on one separate line, as in presentation by nature. Time will tell what becomes of this innovation.