Sometimes companies made an intership from a job because the project is in its early phases, nobody really knows what will happen for this project. it will also depend on the departement finances at this time of the year ( maybe they think they can hire somebody for 6 month, and finally found there is not engouh money).
In your situation : if you are hungry for the position because it is a good company and you don't have really have other good option you can go to the interview and :
-Take the internship and do a goodjob and hope they hire you at the end.
-Show that you are the best candidate, but explain you are young and need to pay your rent and you try to change the intership into a several month contract at minimum wedge. (this is risky, but i have seen it work, for job that required skills on a not famous sofware, the applicant knew he had the perfect qualifications).
Should I restate to them about my actual intentions of applying for a job instead of an internship?
-> confirm on the phone that they didn't make a mistake : "hello dear HR, i received the internship but i apply for a job, would you mind confirm if it is the same position or if there was some changes internally?"
-> if it is not too far from your home ( you don't need to spend a lot of money for the travel), you just go to the interview and make the best of it.You are young, whatever is the result of the interview you will have more interview experience which is good for the futur interviews.