The terms formal and informal networking had meanings in the business world long before the Internet and social networking became such critical aspects of our everyday lives and work. Informal networks may also have referred to friends, family or groups such as the parents of our kids' friends and soccer teammates; at work it's the cliques and groups we hang out with. An informal network arises naturally and is self-made among its members.
Formal networks are those that relate more closely to business or planned events, such as civic club or trade association groups and meetings. At work, they're the people we should communicate with as part of doing business. Formal networks usually are imposed from the top down by, for example, the upper reaches of a large bureaucracy or company hierarchy.
Not much is different in online networking. Consider how formal and informal communication always has flowed in the workplace and how it still flows that way electronically. For example, company memos (formal communications that are official workplace statements) used to be printed and then posted on bulletin boards and placed in managers' and employees' inboxes or mail slots. Today, the leadership who distributes those memos has the same intended purposes and probably distributes them to the same people, but they send their formal communication through e-mail. It's just an electronic version of a formal network.
Informal networks also still exist. In the workplace example, the grapevine, or rumor mill, might have revealed some of the formal network communication (the memo) contents before the e-mails arrived in employees' inboxes. Whether the rumor mill information was entirely correct or consistent never is guaranteed. And in today's technological world, much of the informal networking could have taken place over instant messaging, texts on personal phones or social networking sites away from work. Still, informal networks have their place, too. Social psychology research in the 1930s found that workers tended to be more productive in informal social networks. Businesses afterward became more aware that ideas can move down, up and even sideways, with an emphasis placed on "peer-to-peer" teamwork.