Autarkic economy is simply an economy which does not trade with other countries, or very very little. I.e. It does not import or export any goods.
An example of an autarik economy would be the present day North Korean economy which almost never trades with anyone. Another would be the Soviet Union, which attempted to produce all goods and not trade any goods. Economically speaking this is fooling... Countries should trade with one another to supply goods that they can produce cheaply and should buy in goods that would be difficult to produce.
A small scale peasant economy is simply an under developed economy consisting of mainly primary economic activities such as farming, mining, fishing etc. This economy may or not take part in trade. The term simply describes the scale of the economy.