You got the types of consulting right, but the terminology wrong. Yes, one type of consulting is lending your expertise, another type is lending a pair of hands

You got the types of consulting right, but the terminology wrong. Yes, one type of consulting is lending your expertise, another type is lending a pair of hands. Either of these types of consulting work can occur under "contracting", "freelancing", or other types of business relationships. Often a "pair of hands" consult is hired "until further notice", so it's not always contracting.