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Difference between Cozio's mate and Dovetail mate?

What's the difference between Cozio's mate and Dovetail mate? Wikipedia says "Cozio's mate is a common method of checkmating. The checkmate is an upside down version of the Dovetail mate. It was named after a study by Carlo Cozio, published in 1766." but I don't see any difference in the pictures.
Seems like the same pattern to me. The fact that one is upside down compared to the other doesn't make it a different pattern.
The distinction is totally useless.
Since it is Piemontese like me, let me introduce this great chess player from the past :)

ps (Piemonte) Piedmont is a region of northern Italy

The name of the defense derives from the Piedmontese player Carlo Francesco Cozio (1715-1780), Count of Montiglio Monferrato and Salabue, as well as Lord of Terruggia. In 1766 he published the work Il Gioco degli Scacchi, a new idea of ​​attacks, defenses, and parties of the Game of Chess, a weighty treatise in two volumes and four books that, although not widely distributed at the time, is considered one of the cornerstones of ancient chess literature.

From the competitive point of view the defensive system of the Nero had a decent following in the nineteenth century, having been used also by champions like the American Paul Morphy (1837-1884), the German Adolf Anderssen (1818-1879) and the Czechoslovak Wilhelm Steinitz (1836-1900). In the following century it was adopted, albeit very occasionally, by the likes of the Czechoslovak Richard Réti (1889-1929) and the Franco-Russian Alexander Alekhine (1892-1946), but perhaps the most devoted to this variant was the Polish Xavier Tartakower (1887-1956). However, as the theory of openings progressed, the Cozio Defense lost interest. It is currently difficult to see it in high-level tournaments.
defense Cozio : 1 e4 e5 2 Nf3 Nc6 3 Bb5 Nge7

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