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In a colony, the colonial power controls territory without integrating into hegemon’s nation. The colony may have its own administration and military, but they under the control of the colonial power.

This can be significant. For example the Wikipedia shows for 1870 (using the work of Angus Maddison)

1870	China 189,470	India 134,882[q]	UK 100,180[r]	U.S. 98,374	Russian Empire 83,646	German Empire 72,149[s]	France 72,100[t]	Italy 41,814	Japan 25,393[u]	Spain19,556[v]

As India was actually British colony at the time, the British Empire had a larger GDP than China.