This is a great question. While "experience" in a job requirement generally does refer to professional experience, in a case like your social media example, you should definitely apply. Particularly for an internship, it's likely that they do not actually require professional experience with social media, and are simply looking for the basic skills that you would need to succeed in the internship. (Even for entry level jobs, this may still be the case, although professional experience is of course always very helpful.) For example, I hire interns who work on grants and research funders, and I ask them if they have fundraising experience, but it's not required at all.
In your cover letter and interviews, I would suggest you think about what aspect of your social media experience may be most relevant to a professional setting, for example if you've ever promoted an event via social media, or even if you've engaged with companies online and would like to work on the other end of this. You can highlight those as examples, but definitely don't be afraid to talk about your personal experience with social media as well. Even if you don't think that your experience is exactly professional in nature, you can explain that you are very familiar with these particular social media platforms and would love to use this knowledge to promote the mission of the company to which you're applying.
In general, I would not recommend emailing to ask people to clarify their job requirements. If you think that you could do much or most of the job, you should apply, and explain in your cover letter how your experiences would translate to the particular role. Most people conducting a search for an intern or employee will probably not have time to field questions from applicants, and it isn't really common to ask these types of questions at this early stage in the process. It's important to remember that it's completely possible to get a job without having all of the requirements, especially in areas like years of experience. Just explain why you want the job and how your skills would help you succeed, and you'll have a strong application. Good luck!