Your point about adding more value is extremely valid. Companies often engage consultants when they are doing something new and are looking for expertise in specific areas to fill gaps internally. To me this should be a temporary engagement, and a good consultant will focus on solving the problem at hand and working themselves out of a job (moving on to the next company or challenge).
I did not coin the term "contractor," but yes, it places emphasis on the terms of engagement rather than the work product. But, if you look at common usage you will typically find that contractors are selected for their expertise in a specific area, given specific goals (rather than brought in to solve larger problems), and are often as a group larger in number and engaged longer than a "consultant."
At the end of the day it is really more about adding value than worrying about what you are called. If your skills match the customers needs and you can deliver what you say you can deliver, then it doesn't matter what label your or someone else applies. But, from a positioning perspective this type of differentiation can be important IMO.
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