A scissor cuts the hair very bluntly for a very defined line, as in the classic "bob cut". It also provides a heavy volume line if desired.
A razor cutting tool will provide a very "textured", tapered line resulting in slightly different lengths in the hair ends. This can also provide fullness, but with a much lighter, softer, airy feel and look to the resulting hairline. Soft, airy texture can also be put into the hair with scissors using specialized techniques used by your stylist.