CCP had fought militarily with soldiers against ruling KMT. INC fought mainly using the non-violence and non-cooperation.
INC refused to cooperate with the British during II World War. They launched a Quit India movement. INC spread awareness among people to uphold self respect and to stop exploitation of Indian public by the British. INC protested, held rallies, filled jails, refused to pay taxes, held many rounds of talks with the British etc.
INC fought against foreigners and CCP fought against another party with different ideologies.
CCP had won in a civil war by driving the KMT forces out of the main land. They gained sympathies of people due to atrocities of KMT and ineffectiveness of KMT. CCP conducted rallies like INC did.