Gokon and machikon are both ways of meeting potential romantic partners in Japan, but they work quite differently. A gokon is usually a small gathering where you may know a little about the other participants in advance. A machikon involves many more people, most of whom you have never met before.
A typical gokon is arranged by two organizers, one from each side, who invite several friends or acquaintances to join. The group then meets at an izakaya, restaurant, or similar place to eat and drink together. Unlike an ordinary social gathering, the purpose is usually to meet members of the opposite sex who could become romantic partners.
That does not mean people are expected to choose a boyfriend or girlfriend on the spot. They talk as a group first, and if two people are interested in each other, they may exchange contact details and meet again later. A gokon is better understood as a first step that can lead to a date.
Because the gathering is usually arranged through acquaintances, participants may also know a little about the other group beforehand. You can ask the organizer what kind of people will be coming, for example. Of course, whether you actually get along with someone is still impossible to know until you meet.
A machikon works almost the opposite way. People sign up for an organized event and meet many strangers, sometimes across several restaurants or in one large venue. There is usually much less information about who will be there, but the number of possible encounters is much larger.
So a gokon is a small-scale meeting with a little advance information, while a machikon is a larger event where you meet many more people with little idea who will be there. Both are meant to create opportunities to meet potential partners; the main difference is how those encounters are arranged.
