Correct; the difference is, who comes up with the initiative of a particular person. You come to a firm, talk to some of their guys and you like Alice best, yo

Correct; the difference is, who comes up with the initiative of a particular person. You come to a firm, talk to some of their guys and you like Alice best, you work with Alice -> consultancy. You find Bob somewhere in the world, like him, want to hire him, find a company that deals with the legal details -> remote work agency.