The control of respect to these standards is usually done by an external organization. In the case of Swiss watches, this organization is called COSC – Contrôle Officiel Suisse des Chronomètres. It receives and tests the movements that are later mounted inside these watches to confirm that indeed, they do.
It is something like having your company accounts audited by a CPA. And, as you might suppose, this further processing step has an additional cost which adds to the end price of the product. It does not mean that your watch without it does not work as well. It just means that the watch you are holding in your hands (or strapped around your wrist) has been tested and verified respecting this standard.
The caliber inside the watch is likely to be the same model.
So what is the logical consequence of it all? That you can have your watchmaker regulate your watch to reach chronometer specs (-4/+6 seconds per day) if the movement is good enough to attain them.
This means that this beautiful Oris Artelier Chronometer you see on top is substantially similar to the normal Oris Artelier, except for some cosmetic touches and the fact that its movement, a specimen of the Sellita SW200–1 of the best grade, has been submitted, and has passed, the check of the COSC institute.
Nothing more, nothing less.
You should also know that lots of watch manufacturers use the so-called “ebauches”: that is, watch movements built by specialized companies. Among them, you find famous names such as ETA and Sellita.
And these ebauches come in “grades”. Think about them like they are cars: cars come from the standard, base configuration to the most equipped ones. Ebauches are the same, and usually come in four different grades:
The difference between them is how much they are adjusted after assembly and shipping to the customer. Yes, ebauche-makers do test their movements prior to shipping them to their clients. The only thing changing is the extension of these checks. Standard ones are adjusted in 2 positions for a +/-12 seconds per day performance; Elaborated in 3 positions for a +/-7 seconds per day performance; Top in 5 positions for a +/-4 seconds per day performance; Chronometer respects COSC standards.
So, my end advice is that in most cases, you can buy a chronometer and enjoy a very precise watch and the writings on the dial, or buy a regular model and go to your trusted watchmaker to get it regulated to COSC standards. Your choice. And the final result would be about the same.