Hey there!
A pure market is where the government has little to no government control. It is similar to laissez-faire, meaning hands off, where the government just lets it run, which was instituted in the U.S. by Martin van Buren, although it failed.
A command economy is the complete opposite of the pure market economy. This is where the government completely controls the economy. Communism is a command economy.
If something is traditional, they follow traditions, or follow customs that have been in place for a long time, and a traditional market follows old customs.
A mixed market economy is where free interaction is allowed.
I hope this helps!