Generally agree.
9x19 = 9mm Parabellum = 9mm Luger = 9mm NATO is the baseline caliber.
9x17 is commonly known in the USA as .380 Auto or ACP. 9mm Kurz or Corto or Browning Short in the rest of the world.
9x18 Makarov is really a 9.2mm with .364" bullet instead of .355". Found in Makarov and some other East Bloc guns.
9x18 Police was developed in the early 1970s when the German police wanted a more powerful pistol than .32 Walthers. They bypassed the Police and went on to guns in 9mm Para. You will occasionally see a Walther PP Super and rarely a Sig-Sauer P230 in 9mm Police and even finding the ammo for it is a challenge, so there is little risk of a mixup.
9x18 Ultra was developed in the 1930s so Hermann Goering could have a distinct sidearm for the Luftwaffe. That fell through and ol' Hermann got them Krieghoff Lugers. 9mm Ultra Walther pistols and their ammo are extremely rare.
9x20SR (semirimmed) is otherwise known as 9mm Browning Long. Sweden used the caliber for a while, a lot of their 1903 FNs and Husqvarnas were sold here as surplus but with the chamber sleeved to .380 because there was no supply of ammo. Pity, it is nearly as powerful as 9mm P in a smooth flat gun. There were also a very few LeFrancais and Webley 9mm Browning Longs, but not many.
Then there are the 9x21, 9mm Steyr, 9mm Bergman-Bayard (Largo in Spain), 9mm Mauser Export, 9mm Winchester Magnum, and 9x23 Winchester. Probably some others but those I have seen guns for (except the 9mm Win Mag.)