While tax status (W-2 v. 1099) per se is not that important (my wife works promotions and routinely gets half a dozen of each, or more, every year), the employee v. independent contractor status that they represent can be relevant.
An employee has a common law "duty of loyalty" to an employer, which basically means that the employee cannot directly compete with the employer and cannot undermine the employer, while employed by the employer, even in the absence of a non-compete. The Colorado Supreme Court discussed those duties at length in Jet Courier Service, Inc. v. Mulei (Colo. 1989).
In those cases, it is important legally to know if you have multiple separate periods of employment that begin and end as separate jobs, which basically limits the duty of loyalty to on the job conduct, or if you are a part-time employee for a company for a period of time, in which case your duty of loyalty would ordinarily prohibit you from competing with your employer during the term of your employment.
For example, if you were hired as an employee to come in for three separate weekend jobs, that would have a very narrow non-compete scope. But, if you were hired to come into their officers for five hours a week every week for several months as their part-time IT officer, that would be another story and you would probably be considered an employee for the duration.
In the case of an independent contractor, this would generally only apply of the independent contract was also an agent of the company and only insofar as the scope of the agency extended.
I concur with @user6726 on the copyright issue.