This is a summary of all the major card makers from Japan, listed in roughly chronological order. If I've written a post about the type or maker, I'll include a link to it here.
Feel free to nitpick my selection of sets and makers - my feeling was that these were the most common cards that someone in the US was likely to come across on something like eBay. The only other common cards that I'm really not getting in here are menko and bromide cards.
Kabaya-Leaf (1967): first Japanese card set that looked like an American set. Only released the one set.
Calbee (1973-present): longest active manufacturer of cards. Cards are issued with potato chips
Ed Broder (1974-1976): US serviceman who created low tech b&w sets in mid 70's
NST (1975-1983): stamps issued with albums.
Nippon Ham (1975-1979): cards issued with boxes of Nippon Ham sausage (and yes, that's the same Nippon Ham that owns the Fighters).
Yamakatsu (1976-1981): Many sets and premiums issued with a wide variety of sizes.
Takara (1978-1998): Team sets that could be used to play a dice-based baseball game.
TCMA (1979): 90 card set issued by US card maker TCMA
Play Ball (1987): 42 card set issued by a US card maker
Mermaid Data (1989): cards issued with two small pieces of candy and a sticker featuring a player caricature.
Lotte (1989-1990): Cards were issued with gum. Lotte (who I think is the same company that owns the Marines - and the Giants in Korea) also issued some sticker sets in the late 00's.
BBM (1991-present): The Topps of Japan. I have written extensively about them.
Q Card (1991): Plastic phone card sized cards
Tomy (1993-1994): First competitor to BBM in marketing cards the way cards are marketed in the US
Kanebo (1993-1994): two small-ish sets of "puffy" cards like Action Packed
Future Bee (1998-2001): Made card sets consisting of only players from the Bay Stars, Marines and Swallows. Also produced the Power League game cards in 2000 and 2001 (which featured players from all the teams, not just the three that the regular sets contained)
Broccoli (1999-2001): Made card sets featuring only the Seibu Lions. Was mostly an attempt to capitalize on the popularity of Daisuke Matsuzaka in his first couple professional seasons.
Upper Deck (2000-2001): Issued four sets in two years using the same design as the corresponding issue in the US
Konami (2000-14?, 2018-present): Game cards
Bandai (2010-15): Game cards called Owners League