TL;DR; Students appear to be able to get permission to browse the restricted section at later years, not just to check out specific books. Permission does appear to be needed from a teacher even at later years. Idiotic teachers also appear to give permission to young students with no recourse.
Harry wandered over to the Restricted Section. He had been wondering
for a while if Flamel wasn’t somewhere in there. Unfortunately, you
needed a specially signed note from one of the teachers to look in any
of the restricted books and he knew he’d never get one. These were the
books containing powerful Dark Magic never taught at Hogwarts and only
read by older students studying advanced Defence Against the Dark
Arts. - Philosopher stone(emphasis mine)
This quote heavy implies that has an older Student with permission can look at any book in the restricted section, and need not get note by note approval for each book.
This would fit in nicely for both Hermione and Riddle who were both top of their class and could easily have obtained such access in later years to further their studies.
As year 2 students attempting to get a restricted book, it was most likely better for Hermione to get said specific book listed on her note to not bring too much suspicion down on herself.
There was only one way to get out a book from the Restricted
Section: You needed a signed note of permission from a teacher. -
Chamber of Secrets
Again it never specifies the note need include the book title.
In year 4 Harry seems to get a note from Professor McGonagall that allowed him to browse in the restricted section
So Harry, thinking that he would soon have had enough of the
library to last him a lifetime, buried himself once more among
the dusty volumes, looking for any spell that might enable a
human to survive without oxygen.However, though he, Ron
and Hermione searched through their lunchtimes, evenings and
whole weekends – though Harry asked Professor McGonagall for
a note of permission to use the Restricted Section, and even
asked the irritable, vulture-like librarian, Madam Pince, for help
– they found nothing whatsoever that would enable Harry to
spend an hour underwater and live to tell the tale. -Goblet of Fire
This shows he had no idea what book he needed, so it was most likely a blanket permission to browse.