No, it's like this:
G, PG, PG-13 = anyone can see these, the different ratings are guidelines
(G= General Audiences, PG= Parental Guidance, PG-13 = Parental Guidance/Not recommended for those under 13)
R = Under 17 must be accompanied by their parent or guardian, not just any adult
NC-17 = only those 17 and over are admitted
Now, whether or not theaters enforce the R-rating is another story and Hollywood NEVER makes NC-17 movies because it scares audiences away (people mistakenly equate it to XXX).