Because hosts (computers) of an intranet are limited to a single network, security exposure is somewhat limited. A host on the Internet, however, is exposed to other hosts that are on other networks. Just based on the number of hosts, any host on the Internet has much more security exposure than a host on a intranet.
In terms of organizational threats, almost all hosts belong to the same organization, be it a school, a corporation, a government branch, or a small room of gamers. Hosts on the Internet, however, belong to many different organizations and individuals, many of which can be criminal or adversarial.
Does this really mean that hosts on an intranet does not need as much protection as a host on the Internet?
The answer is absolutely not!
In an organization, there can be subversive individuals, disgruntled employees, industry spies and etc. Although the number of potential threats may be fewer, it only takes one successful hack to get a host compromised. As a result, the consideration of security should be the same on any networked hosts, regardless of whether they are on an intranet or on the Internet.