In Hinduism, Karma, the law of cause and effect, is very important because of the atman, the eternal self, which is reincarnated over and over until it has reached the point of freedom from samsara, which is known as moksha. The Hindu belief of karma is central to their understanding of reaching or attaining salvation from suffering. Turns on the wheel of samsara are a cause of great suffering. Karma and Dharma, which is ethical duty are the two principles that link the divine with the earthly. in order to achieve moksha, the Hindu has to work through the accumulated effect of all his/her past lives, the scorecard, is the karmic record, which goes with the eternal self from one life to another. It is only in the human form that a Hindu can affect his/her karma. If an individual has accrued bad karma, it is necessary to perform good acts, according to the dharma, or moral laws of your caste, gender and occupation in life. This is difficult, since some castes are destined to do the dirtiest jobs in society, therefore acquiring bad karma from these actions.
In Buddhism, there is no self, anatta, therefore, the idea of karma is not the controlling force that it is in Hinduism. Karma has an effect on our present life condition, but Buddha taught that we have more control over our life than Hinduism allows. If we are experiencing trouble in our life, it is more likely because of something we have done today, not because of the baggage of bad karma held over from previous lifetimes
Karma can be defined as the law of causation, basically "As you sow so shall you reap"
In Hinduism Karma forms part of the three yogas,that is different ways to attain God. The Karma yoga is the path of action (selfless) for the attainment of the Supreme.
The element of Karma is also used by Hindu scriptures to regulate the behaviour of people. It is associated with the belief that all actions performed are reflected on our souls and due to this we can remain trapped in the cycle of birth and death.
In Buddhism, the element of the soul is rejected, so karma is mainly used to explain transmigration.This can be further explained through the 12-chain links which elaborates on how the cycle of birth and death occurs.
So basically,the diiferences between the karma of Buddhism and Hinduism can be explained on their beliefs concerning the existence of the soul.