In an internship, you are usually connected with a mentor who will be responsible for teaching you about the job and give general guidance. So you are not expected to know everything about the job, but to know enough basics to be a success. For example, in an internship in a publicity and marketing firm, you would be expected to have a good grounding in language and writing basics, but they would help you learn the more nuanced parts of how to do the job. You might start off as a copyeditor or proofreader and then, as you learn, move up to do more difficult work such as writing or designing campaigns.
In some cases, internships can come with a small salary or stipend. In many careers, in many states, an intern is considered an employee for purposes of legal liability and worker's protections. This makes a difference in jobs such as where personal care is given to clients, so an intern would be given the training to give a good standard of care.
Volunteer work can give very valuable knowledge and help you to form connections, but might not be as closely supervised and would not be as likely to advance to more difficult learning situations. Volunteer positions are usually easier to get and require less of a commitment - and the organization might likewise have less of a commitment to you.
In either volunteer work or an internship, your attitude and hard work can make a big difference. You may be recognized with greater responsibilities and challenges in either case. Both will look good on your resume and both can provide valuable learning and connections.
Get busy now and put together a resume that highlights your skill, abilities, and interests.
Search for BOTH!! Apply to every internship and volunteer opportunity that is of interest, and see what is offered to you. It could be that a great volunteer position will be better for you than an internship that does not really interest you.
Come back here and ask a more specific question if you are trying to decide between two or more offered positions.
The most important consideration is to do something this summer that is engaging and challenging.
Go for it!