I spent 6 years as an intern at my current company. I put in my miles, paid my dues, and proved myself enough to secure a full time position. Many people coming out of college have experience with internships. An internship allows you to get the near full experience of what it's like working for a real company. Sure, you might have gotten coffee and lunches for your superiors during your time as an intern, it was truly meant to prepare you for the real world. A full time role might have some familiar feelings to your internship experience, but there are some major differences as well.
Moving from an internship to a full-time role carries advantages for both you and your employer. It's extremely beneficial to come into a situation and know the environment. You already know how your company does things. Adjust to the differences of a full-time role and you'll be well on your way to enjoying your success.