It's not exactly "consulting vs contracting", its "hiring a single person vs hiring out a project". Many "consulting" shops do what you call "contracting", because "consulting" is a more "elite" word.

But a single person can be a "contractor" too.

(At big companies and non-IT fields, a contractor is often used for temporary professional employee-type labor for flexibly scaling the labor force that includes employees doing the same job, but a consultant is someone who provides a skill you don't have in house at all.)