What is the difference between mixed, command and traditional economy?
I'm not sure what you mean by "mixed command..."
In a command economy, the government determines how the three basic economic questions (what to make, how to make it, who to make it for) will be answered. So, economic planning is done by the government.
By contrast, in a traditional economy, the questions are answered by tradition -- people do things the way they always have. So people make what their parents made and make them in the same ways.
A third kind of economy is a market economy where consumers decide (through their buying choices) how the three questions will be answered. So what consumers want gets made and it gets made in the way that consumers want.
In usual economic terms, a mixed economy is one which has elements of at least two of the above kinds of economy.
It appears the question has mixed up its terminology. Some economists believe that economics is concerned with understanding how economies determine what goods to produce in goods in what quantities, what resources are used for producing the required goods, and how the goods produced are shard by different members of the society. Further economists identify two broad approaches that may be adopted for taking such decisions. Depending on the approach used by an economy it is described as market economy or command economy. It is also possible economies to uses some combination of these two basic approach. Such economies are called mixed economies.
In a market economy, individuals and firms make decisions about their production and consumption depending on what they consider to be in their best interest. This attempt to maximize personal gains taking into considerations price, costs, profits, and losses, combined with mechanism of supply and demand, results in the economic decisions of the economy as a whole. It is presumed that this mechanism automatically results in maximizing the good of all the people in the society. While there is some truth in this assumption, it is not absolutely correct.
In a command economy all economic decision are supposed to be taken by a centralized authority such as a a government to achieve good of the whole society in a deliberate and planned way. In such an economy the resources of production are typically owned by government, and the goods produced are supposed to be shared equally by all members of the society. While this approach is very attractive in terms of its design and logic, it presents major problem of implementation. One grand design ensuring smooth working of entire economy maximizing combined good of all the members of the society is too complicated to be worked out. Centralized implementation and control of such plans pose additional problems. Also, there is no way to prevent corruption among few people who enjoy enormous power under such a system.
In this system of classifying types of economies, there is no specific type called traditional economy. However, Traditionally economies have leaned more on the side of market economise rather than command economies. After Russian revolution, inspired by Ideas of Karl Marx there was a marked swing in many countries towards command economy. However, many countries that had tried to follow the command economy are again moving towards market economy. At the same time countries that traditionally prided on their free market economies have realized the need for some centralized control and have adopted many elements of command economy also. Thus almost every country in the world today is following a mixed economy model wit some leaning more on the market economy side and the others on command economy side.