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.)

I recently accepted a job at a consulting/contracting firm for a specific contract as a data scientist. I had three separate interviews with the company I'd be working indirectly for, and I wasn't the only one they'd been interviewing. There'll be no switching me out for a junior.