The answer to this question can be found in Chapter 14. There is a nice summary of the basic aspects of the various types of society in Table 14.1. We can start by saying that a tribe is the second smallest type of society while a state is the biggest. Most of the differences between them stem from and/or contribute to this fact.
Tribes are very small. Tribes typically number in the hundreds of people. This is in contrast with a state, which, according to Diamond, has at least 50,000 people. Because a state is so much bigger than a tribe, the basis for the relationships between the people of the state is very different from that of the tribe. The people of a tribe are connected to one another through membership in clans. By contrast, the people in a state are not related to one another and are connected only by the fact that they live in the same place. Because of this, government in a state is much more formalized. Disputes are settled by laws and judges. There is a centralized government and a large bureaucracy. By contrast, since people in a tribe are closely connected to one another, they have an egalitarian system of making decisions and conflicts are settled informally through networks of kin and friends.
In short, tribes are small and informal societies whereas states are large and formal.