9 mm = .354 inches. Most 9 mm bullets actually measure from .355 to .357 inches in diameter.
A 9 mm diameter x 17 mm long round has many common names.
Among them are:
.380 ACP (Automatic Colt Pistol)
9 mm Corto
9 mm Kurz or Kurtz
9 mm Browning Short
".380 ACP" is the term most commonly used in the U.S., the other terms are used more commonly in Europe and elsewhere.
A 9 mm diameter x 18 mm long round is often called:
9 mm Makarov (actually 9.2 mm)
9 mm Police
9 mm Ultra
A 9 mm diameter x 19 mm long round is often called:
9 mm Parabellum
9 mm Luger
9 mm NATO
This is the most common 9 mm round. When the term "9 mm" is used alone, this is usually the round that is being referred to.
There are also other less common 9 mm rounds:
9 mm x 20 mm (Browning Long)(SR)
9 mm x 21 mm (IMI)
9 mm x 23 mm (Largo)(Steyr)(Bergmann-Bayard)
The .357 caliber bullet, as in ".357 Magnum (9 mm x 31 mm)" and ".357 SIG" are also 9 mm bullets.
The .38 caliber bullet, as in ".38 Special (9 mm x 29 mm)" is also a 9 mm bullet.
Most .357 caliber revolvers will also fire .38 Special rounds.
There are also other rounds with this same diameter bullet:
.38 S&W (Colt New Police)(Colt Super Police)
.38 Super Auto
That's all I can think of for now. I'm sure others can add more.
Very confusing and probably more than you'd care to know.