What do mixed and command economies have in common?
What mixed economies and command economies have in common is that mixed economies have some aspects of command economies in them. A mixed economy is generally a combination of a market economy and a command economy (possibly with a few aspects of a traditional economy thrown in).
In a pure command economy, the government makes all of the economic decisions. It decides what goods and services will be made, how they will be made, and who will get them. In a pure market economy, consumers make all of these decisions as a group through their purchasing decisions. In a mixed economy, there are aspects of both.
The United States has a mixed economy. Let us look at some ways in which it is like a command economy. The government in the US decrees that K-12 education will be produced in public schools and that all children under a given age will receive it. The government decrees that police and fire services will be provided. In my county, the government provides electricity through a public utility district. The government decrees that some people will be paid to make rules that protect the environment and to make sure that other people obey those rules when they do things like building homes. All of these are examples of the government saying what will be produced, how it will be produced, and/or who will receive it when it is produced. The major thing that a command and a mixed economy have in common is that the government does this to some degree in both types of economies.