Just a couple of others - - -
In the late 1960s/ early 1970s, Super Vel cartridge company (Lee Jurras, prop., Shelbyville, Indiana,) offered the first "Modern" 9x19 loads. They had a 112 gr. jacketed soft point and a 90-gr JHP, both of which were reputed to be pretty hot. I was impressed with the JHP when I had to destroy a sick house cat and the bullet fragmented on the cat's head. I was unaware of the importance of proper penetration at the time.
I later had a difficulty with a couple of robbers and learned the 90 gr. JHP wouldn't properly penetrate either automotive safety glass or a trunk lid and seat back . . . . Swore off the light bullet loads thereafter.
Illinois State Police adopted the S&W M39 early on, and got Winchester to make up a special 100 gr. JSP load for their exclusive use. I never saw it offered for commercial sale.
In the mid-1980s, a friend special ordered some sub sonic 9 mm FMJ. I don't recall the name on the boxes, but bullet weight was 150 to 160 gr, NOT the later-popular 147 gr. You may still find a few rounds of KTW ammo, with green Teflon coated bullets, and Arcane, with lathe-turned bronze bullets. These were developed for penetration of vehicles, just prior to the furor over "cop killer" bullets, supposedly designed to penetrate soft body armor, and hence outlawed.
Once you start looking at foreign surplus ammo, you're apt to find an even wider assortment. Some stuff reputed to be Czechoslovakian submachine gun ammo, with steel jackets, used to be the thing for extra penetration. There was a lot of WW-II German ammo of around 100 gr. weight, made of sintered iron, also.
I guess my last three paragraphs are outside the scope of your original question, "What kinds/types of 9mm ammo are there?" You probably just want information on currently available commercial types, huh? Almost forgot- - - There's a blossoming field of "low enviornmental impact" bullets, using sintered iron and copper bullets - - One such brand is, I think, Firefrangible. Another is Delta Frangible Ammunition (DFA.)
Best,
Johnny