There is no such thing as a "9mm Beretta" cartridge. Beretta firearms were manufactured in 9x19mm (also known as 9mm Parabellum or 9mm Luger), 9x17 (also known as the .380 ACP), and some models are made in 9x21 IMI for countries which prohibit civilians from owning firearms chambered in military calibres. The cartridge appropriate for your Beretta 9mm should be marked on the frame and slide.
Glock is a brand. 9mm is a caliber size. So, there is no difference between a 9mm glock and a 9mm of another brand as far as caliber size.
No such ammuntion as 9mm rugger
No. There several different case lengths that accept a 9mm bullet. 9mm Kurz is not the same as 9mm Luger, which in turn is not the sameas 38 super, 9x21, 9x20, etc. The diameter is the same, but the cartridges are different sizes.
No. Not all 9mm cartridges are the same. 9x19 (a.k.a., 9mm Luger, 9mm Parabellum), for example, is different, hence, not compatible with other 9mm cartridges, such as the 9x17 (a.k.a., .380 ACP), 9x18 Makarov, 9x21, 9x23 Mauser, etc.
The .380 ACP is a type of 9mm... 9x17, and is sometime referred to as the 9mm Short or 9mm Kurz. It is NOT the same as the 9mm Luger/Parabellum (9x19), and it is NOT compatible with any other type of 9mm cartridge (such as the 9x19 Luger/Parabellum, 9x18 Makarov, 9x21, 9x23, 9x25, etc.).
9mm = .355 40 cal = .40
No. There are several different calibers that are called 9mm. These calibers are not interchangeable. A quick rundown of 9mm pistol cartridges: 9x17 also called 9mm Kurz, 9mm Short or .380 Auto 9x18 Makarov, also called 9mm Makarov 9x19 also called 9mm Luger, 9mm, 9mm Para, 9mm Parabellum 9x21 also called 9mm IMI 9x23 also called 9mm Long, 9mm Largo
Same round, different weapon design.
Case length.
Different makers. The cartridge used is the 9x19.
Not a good idea. Shooting 9X19 in a 9X21 chamber puts a lot of extra pressure on the extractor causing it to fail prematurely.