How did Mao’s Great Leap Forward differ from Deng’s Market Socialism? How were they similar?

The Great Leap Forward was a radical attempt by the Communist regime under Mao to change the whole nature of the Chinese economy. Mao wanted China to become an industrialized country in order to create a genuinely socialist society. He also wanted China to overtake the Western capitalist nations in terms of industrial output. As the People's Republic was a predominantly agrarian country, this was a highly ambitious goal.
Unfortunately, it was too ambitious. The policy was rushed and badly planned from the start. Lack of resources, skill, and expertise meant that mass industrialization never stood a chance of getting off the ground. In fact, Mao distrusted technical experts, seeing them as an intrinsic part of a Soviet system he had come to despise. Instead, he believed that mass mobilization and ideological fervor would suffice.
In practice, the policy was a human and economic catastrophe on an almost unimaginable scale. In addition to the poor planning and lack of resources, millions of peasants were removed from the land and forced to work in primitive backyard steel furnaces. The huge sudden drop in the rural workforce, coupled with the collectivization of agriculture, led to massive food shortages, which in turn led to widespread famine. Tens of millions perished as a result.
Deng's policy of market socialism was similarly radical and ambitious, though it had completely different goals in mind. Like the Great Leap Forward, it also represented a top-down approach to economic affairs; like the Great Leap Forward, the policy was designed to help the People's Republic catch up with, and eventually surpass, the capitalist West. At the heart of Deng's policy was a desire to maintain the Chinese Communist Party's iron grip on political power while instituting market-based economic reforms. Broadly speaking, this is the same strategy used by successive Chinese leaders ever since.
Under Mao, the very idea of introducing market forces into the economy would have been unthinkable. But, as he explained, Deng saw no contradiction in pursuing such a goal:

Practice of a planned economy is not equivalent to socialism because there is planning under capitalism too; Practice of a market economy is not equivalent to capitalism because there are markets under socialism too.

Whereas Mao's Great Leap Forward sought to increase government control over both the political system and the economy, market socialism under Deng ceded control over the production and allocation of certain goods and resources to the market while retaining one party rule.
Unlike the disastrous Great Leap Forward, Deng's market socialist reforms were largely successful. They set in motion a process which has enabled China to become a leading player in the international economy, enjoying unprecedented levels of economic growth and prosperity. Despite these radical changes, one thing that has not changed is the unchallenged rule of the governing Chinese Communist Party. For Deng, this would have been an even greater sign of his policy's success.