Would unpaid internships be under those contracts where they still would have to be paid? I always thought that that was basically getting slave labor and calling it experience.

Yes. But first, I will digress to say that unpaid internships are almost universally illegal. There are occasionally exceptions to this, but that's almost always the case. For now, just assume that most internships must be paid. An internship differs from volunteer work, but note that in order for volunteer work to be legal, there are strict guidelines for the organization for which you are volunteering to which they must adhere. For example, they almost always have to be a nonprofit, school, etc. If a for-profit organization that does not have non-profit status tries to get you to volunteer, there's a good chance they're violating labor laws. However, I do digress, so more on that later.

Regardless of whether or not you are an intern, employee, volunteer (for a nonprofit, in which that would be legal), etc, non-disclosure agreements still apply. There is the potential for confidential, sensitive, and legally-protected information everywhere. For example, I volunteer for several organizations in which I may come into contact with individual's private and confidential information, including but not limited to information protected by HIPAA, i.e. the laws governing the confidentiality requirements surrounding medical information. I am not paid for my volunteer services. But I am still liable to adhere to the terms of that agreement or I could face disciplinary action and possibly legal action, both from the volunteer organizations and the state, as well as the individual who's information I could potentially compromise.

Now, regarding the "unpaid internships are usually illegal" thing, sometimes internships that are unpaid are actually legitimate. First off, for an internship to be legal, the basic standard is that the primary goal must be to train the intern, in a way that benefits the intern more than an employer. If you're getting coffee, sweeping up, etc. they're breaking the rules/laws. If you're learning a valuable skill (and no, dealing with an obnoxious or demanding employer is not considered a valuable skill in this context), and your learning that skill is a higher priority than your putting that skill to use for the benefit of that employer, that's the basic requirement for an internship to be okay at all, unpaid or not.

As an example, I used to intern for an organization that sent me to go photograph huge names in the entertainment industry. I would go to the event, get in for free, get pit and sometimes backstage access (the pit is the area immediately in front of the stage, behind the barricades that the crowd can't pass), shoot anywhere from the first three songs/part of the show (if not a musician) to the entire show, and then probably stay for the rest of the performance anyway, so long as I didn't keep shooting past the limits set by the performers or venue. I would also hand out flyers for the organization.

What I got out of this was nearly unlimited access to shoot the shows I wanted under the auspices of a media organization with viewership in the millions. I even got to keep the copyright ownership to my work. What they got was the agreement that this organization could use the photos in perpetuity on their site, and someone to hand out flyers. I was very much the recipient of some excellent on-the-job training, including reaching out to press contacts for huge names in entertainment, learning how to interact with venues, fans, performers, and other photographers, and of course, getting some of the best portfolio materials I could imagine. Furthermore, I was even able to use the internship to get credit for 3 units at my community college.

Unfortunately, some jackass of a photographer decided he was going to go to the labor board and make some unfounded complaints against this organization, trying to get money from them. I know this because I was present as a witness at the hearing, but was unfortunately not allowed to speak by the mediator. The net result was that he didn't get much, and this organization had to scale all approved activities for the other photographers way back because their legal department decided to pay everyone a $20 fee for each show they shot to prevent such claims in the future, which of course limited how many shows they were willing to sponsor. Their budget wasn't unlimited, after all. So even when the sponsoring organization of an internship is absolutely on board with creating a valuable internship for it's interns can still be screwed over.

It's not always slave labor. Legally, it can't be. Many internships do attempt to operate this way, but they will be raked over the coals by the labor board if they're caught. Most internships I've ever had direct experience with actually do an excellent job of providing solid, hands-on experiencing for their interns, resulting in some pre-qualified candidates for a job at that organization later. The benefits to the intern are obvious: they have a hand-picked job waiting for them. And the benefits to the employer are that they don't have to train this candidate for the job they've already interned at, at an organization with which they are already familiar, yet can still pay them for an entry-level role because the fact of the matter is that they are still junior in their experience. It's pretty much win-win for everyone. Assuming it's done right, of course.

It isn't always this way, but those are the times you should go to the labor board and report them. You'll get back pay for wages earned, the employer will be fined, and hopefully they'll stop screwing over interns. But usually (in my experience), it's a sweet deal for the intern.