Just to clarify... Are you asking how the Mongols invaded and conquered china in the 1200's while the Japanese couldnt in 1937 ?

First and foremost, the Qing conquest took decades; starting with raids over the border and attacks on Ming tributaries in the early 17th century, the Qing only finally consolidated control over the whole country in 1683, when the Revolt of the Three Feudatories was put down.

Furthermore, they relied heavily on defectors from the Ming to supplement their martial skills; Han bannermen and the Green Standard armies made up the overwhelming majority of the Qing's forces, and provided all of the guns and cannon needed for the conquest.

Native Chinese were already heavily divided at the time; cooling global temperatures in the 17th centuries meant poor harvests, which meant soldiers often went unpaid. One such detachment was led by Li Zicheng, who captured Beijing and overthrew the Ming Dynasty proper, thus dividing an already chaotic realm before the Manchu invasion.

The Qing also legitimized their rule much better than the Japanese; when they took Beijing, they officially claimed the Mandate of Heaven, and within a year they were the ones holding the Imperial Examinations, a key mechanism for Imperial control. By contrast, the Japanese were unable to establish the legitimacy of their regime among their new imperial subjects, since the fall of the Qing led to a nationalist paradigm shift away from the old Confucian narrative of Heaven ordering obedience to the most fit ruler, who, in the context of the Manchu Conquest, was obviously the Qing.

The Manchus took advantage of the existing Chinese political collapse in the 1640s, by the time of the invasion the Ming dynasty had already being overthrow by Li Zicheng's peasant rebellion. The last Ming emperor had committed suicide as Li's army entered the capital Beijing and Li had proclaimed himself the emperor of the new Shun dynasty. Wu Sangui, a Ming general guarding the frontier against the Manchus, made a deal to let the Manchus through the Great wall in order to crush the rebels. The Manchus then advanced into a power vacuum within China and conquered it, bequeathing huge tracts of the south to Wu Sangui and his allies (they would rebel and be defeated number of years later).

The Mongols also conquered a China that was political divided, at the time of the Mongol invasion northern China was under the control of non-Chinese Jin dynasty, while the south was under the control of the native Song dynasty. The Song actually initially allied with the Mongols against the Jin, only to become the new Mongolian target once the Jin fell.

The Mongols were also fairly unique in world history as an effective military force relative to their contemporaries, something which was not realized by the Japanese centuries later. But even so it took several decades for the Mongols to conquer southern China.

The Japanese by contrast invaded a China with some semblance of political unity under the KMT, in an age of modern nationalism in which conquered peoples are far more likely to resist the invaders, and in an industrial age when mass conscription armies were the norm. Small forces were no longer capable of defeating far larger ones in the same way that the Mongols were.

One should also not overstate how industrialized Japan was either, Japan actually had a relatively weak industrial base in the 1930s-40s (as WWII will show) and it had an army based on light infantry instead of armored formations as the Germans the Soviets had. One should not overstate Chinese weakness either, China did experience significant industrial growth in the decade prior to the Sino-Japanese war.