Of the four economic systems, what two are similar and different?

Of course, no two of the four economic systems are exactly the same. If they were the same, they would not be different systems.  Of the four, mixed economies are somewhat similar to both command and market economies. Traditional economies are very different than both command and market economies.

Mixed economies are typically a blend of command and market economies with a little bit of traditional economy thrown in.  Some mixed economies are closer to pure market economies, like the US while others, like Sweden, are closer to being command economies. Mixed economies are like market economies because they typically allow people and markets to make many choices. However, they are also like command economies because they include some amount of government control over the economy.

Traditional economies are very different from both market and command economies. In market and command economies, there is no room for tradition.  People pick their jobs in a market economy based on what they can do that will make the most money, not on what tradition says they should do.  In a command economy, decisions are made based on what the government wants, not on what tradition says.  Command and market economies are very modern economic types while traditional economies are old-fashioned.  For these reasons, traditional economies are very different from both command and market economies.