The word "consultant" is largely meaningless in the debate about employee vs. contractor. I know of at least one large company that officially uses the word "consultant" to describe any person doing exempt level "managerial" work but has no staff. I also know consultants who work on a business to business relationship with companies and is, quite clearly, a contractor. In the end, you are either issuing a w-2 or a 1099 and a consultant could receive either.
I was, at one time, working as a freelance HR consultant. I offered people 3 options. 1) pay a large fee up front (to cover all my insurance costs), 2) hire me through a staffing agency (high per hour cost but offsets my liability), 3) hire me on a temporary basis (lowest cost for them, lowest liability for me). I have done many gigs as a consultant as a temporary employee directly hired by the company, filling out all their paperwork, etc.