While BBM was the first company to sell baseball cards the way they were sold in the US (10 or so cards to a pack rather than 1 being sold with some sort of food), they weren't the last. The next company to try it was Tomy in 1993. Their first set was 410 cards plus 81 puzzle cards (which made up nine different puzzles). Most of the cards show a photo surrounded by a colored border. Each card also has the initials "I.D." prominently on the front - I have no idea what they stand for. Like the 1993 BBM set, the most highly sought out cards are the rookie cards for Ichiro Suzuki and Hideki Matsui. Unlike the BBM sets of the time, the cards were the standard US card size - 2 1/2 inches by 3 1/2 inches.
Here's a couple example cards of Susumu Mikoshiba (#125) and Takuro Ishii (#232):
A number of the cards feature border-less, multiexposure photos (a la some of the early Upper Deck sets), labelled on the back as "Action Series". Here's one of Jack Howell (#392):
Oddly enough, at least one of the "Action Series" cards commemorates one of the Hawks players who played for the Salinas Spurs in the California League in the early 1990's. I don't know if there are any more of them than this card of Motoi Ohkoshi (#401) who played for the Spurs in 1992, the final year they had an affiliation with the Hawks:
According to Gary Engel's "Japanese Baseball Card Checklist and Price Guide", the set also includes team checklist cards and four card Japan Series subset (don't know if the Series in question is the 1992 or 1993 Series - both of which were the Lions and Swallows). I don't have any those cards, so I can't show you them.
I got a question in a comment recently about whether or not the Tomy set had multiple series. I think the answer is no, but the set did have multiple printings. On the lower right side of the back of each card is either "I.D.69-001" or "I.D.69-002". This is sheer speculation on my part, but I suspect that set got issued in two printings with this value changed between issues. There are also three "error" cards from the first printing that appear to have been replaced in the second. Here's the back of Ichiro's card (#102) where you can see the "I.D.69-002" on the bottom right:
Tomy followed up in 1994 with a smaller (288 cards including 45 puzzle cards) set. The first 72 cards of the set were "Kira" cards showing the player superimposed on a sparkly silver background - a preview of the kind of thing that BBM would do a couple years later with the Diamond Heroes sets. Here's Kimiyasu Kudoh's card (#54) as an example:
The remainder of the cards (except for the puzzle cards) showed full bleed photos of the player. Here's Takahide Itoh's card (#106):
Oddly enough, although the set does not include a card for Ichiro Suzuki (Tomy not being as prescient as the Hilo Stars team set manufacturer), it does feature three cards (including two "Kira" cards) for Mac Suzuki, who at the time was playing in the US minors, having signed directly with Salinas in 1992 independently of any Japanese teams and played for San Bernardino (where Salinas moved to in 1993) and Riverside (after signing with the Mariners organization in 1994) in the California League.
For whatever reason, Tomy ceased to produce sets after 1994. I suspect that it is not a coincidence that in 1995, BBM increased their card size to the standard 2 1/2 by 3 1/2 size, same as Tomy's. Also in 1995, BBM had puzzle cards in their set for the first time (they would return in the 1996 set as well). And as I mentioned before, the "Kira" cards from the 1994 Tomy set resemble the kind of cards BBM would start producing in 1996 for the Diamond Heroes set and later the Touch The Game sets. So while Tomy may be gone, they may have had an influence on BBM.