I can't tell you the reason why it has become popular in the West beyond "cultural diffusion" but I am a Buddhist so I can tell you about the difference between Eastern and Western ideas of karma.

In the traditional sense, karma is what determines where you will be born in the next life in both Hinduism and Buddhism. There is a sort of hierarchy in the caste system that extends beyond just humans. There are 5 distinct realms which a person's soul can transverse. The human realm is the one in which we live, and has several levels, with priests at the top and 'untouchables' at the bottom. Below 'untouchables' like butchers and sanitation workers are animals. Within the animal realm, there are also different levels. A dog would be above a slug, for example. Above humans are the gods. There is also the realm of 'hungry ghosts' in which a soul is never satisfied and constantly craves no matter what they do. Below that is a sort of hell realm of neverending suffering. Unlike the Christian hell, however one can get out after their 'sentence' has been served and their bad karma has been diminished enough to allow them to 'upgrade' realms.

This is very different to the Western idea of karma which is fairly instant, and punishes people in this life rather than the next. My best guess as to the reason for this difference is the permanence with which Western religions treat death and the afterlife.