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One of the main differences between the two genres can be found in their names. A horror film wants to horrify  audiences whereas a thriller film only seeks to thrill.  With horror, the focus is on scaring people.

I'll add one more obvious point as a bonus: At their most basic level, horror stories attempt to elicit a fear response (whether through disgust or terror) whereas thrillers simply seek to grip and excite. Both genres feature many overlapping suspense elements, but their focus can be very different.