* "Gacha" is basically a mystery prize. Pay 1 token, get 1 random thing from a pool of options. Generally no published odds.
* "Kompu Gacha" is a system where you have to collect a set of specific prizes from the pool, which you can then turn in to obtain a very desirable item. Again, odds not published. And as you might expect, 1-2 of the items will be extremely rare, meaning that most people end up with an almost complete set, and a strong compulsion to open just one more prize to see if it'll complete it, but with no guarantee you'll ever complete it.
* "Box gacha" has a fixed, depleting pool of prizes with a known distribution; they come out in a nominally random order, but you can buy every prize in the pool and guarantee that you'll get the reward.
Once you start to look around, you'll see the mechanic and variations on it everywhere. McDonald's runs a popular Monopoly game that's a pretty classic kompu gacha. Tons of modern computer/console games have some form of loot crate which works like that. One I've been seeing a lot is multiple currency tiers, where an easy/free currency can purchase draws from a low value prize pool, and a harder/cash currency can purchase draws from a high value prize pool. Another trick is to have an armour set that works really well together, where most pieces can be obtained (with effort) for free, but one piece can basically only be obtained as a rare prize that costs cash per draw. You grind out getting most of the armour, then realise it's mostly useless without the helm of power (or whatever), and so you buy just one prize draw to see if you get lucky and complete the set so all your work wasn't for nothing. And then one more draw. Good way of drawing in "gamers" who might resist a cruder form.
Even Overwatch has it: During their periodic holidays, there's a new loot crate which you can earn via playing games (very slowly) or purchase for cash. The new loot crates have a chance of containing new cosmetic items (costumes, emotes) that are only available during the holiday. And that's the only way to get the items, and the holiday only comes up once a year. So if you really, really want the new Mercy costume, you'll end up buying packs of crates and opening them in the hope that this batch will have the costume. Or this one. Or the next one. Anecdotally, most people end up paying way more for the items they want than they would have if they were just listed in a store for dollars. (There's zero play to win in Overwatch; it's just cosmetic. But it's still a bit sleezy.)
As for links, maybe:
http://www.serkantoto.com/2012/11/01/kompu-gacha-package-box...
http://www.serkantoto.com/2016/03/14/gacha-monetization-japa...