Horrible and horrific are both related to horror but the words have different connotations. While horrible can be used to refer to something that is not liked or is disagreeable, horrific is a somewhat stronger adjective used to describe things which upset and frighten by their sheer mention. For example – "A horrible meal" and "A horrific war".
At times, both "horrible" and "horrific" can also be used to mean more or less the same thing, e.g. A horrific/horrible illness.
edit Difference in meaning of Horrible and Horrific
Horrible is most often used to imply unpleasantness and disgust but can also be used to convey horror or fear. The word can be used as a noun and an adjective.
horrible as a Noun The use of "horrible" as a noun is fairly rare. A person wearing a funny or gross costume in a parade of horribles is called a horrible.
horrible as an Adjective
- Causing unpleasantness or disgust. e.g. What is that horrible smell?
- Very wrong or erroneous: e.g. She had a horrible suspicion of elves living in her attic.
- Causing horror or shock: e.g. A horrible train accident.
Horrific is always used an adjective.
- Something that is horrifying or causing horror and fear. e.g. The holocaust was the most horrific phenomenon of the twentieth century.
edit Differences in Usage
Horrible is a word commonly used in normal everyday conversations in English. The food could be horrible or you could say that someones sense of style is horrible.
Horrific is a more formal word finding presence in newspapers and books to describe brutal crimes or fearful tragedies.