Wherever you go, dance instructors and studios have different definitions of what a "beginning" or "intermediate" class is. Even within a single studio, teachers may disagree on what should be included in each level and whether that definition should apply to kids or adults.
At Le Studio where I teach, all three of the ballet instructors (Susie, Melissa and me) are in continual discussions about what each of us includes in our classes and what we expect to see from students who graduate from one level to the next. It's important that we agree on what material and vocabulary are in each level so students have a program to follow.
Some programs of study such as RAD have graded levels and students must pass intense examinations in order to progress. However, for most of the classes you find in the United States, where a combination of French and Russian styles are taught, where a little Balanchine may be introduced to older students or adults, the level distinctions are a little more vague.
Among my classes for adults, I expect beginners to know all their positions, all head and arm movements, basic steps like pas de bourree, pas de chat, and balance. They should be able to do a single pirouette en dehors and en dedans. Across the floor they should do pique turns, chainees, chassee, saute arabesque, and they should know the difference between saut de chat and grand jete. In the center, I expect changement, assemble, glissade, echappe in 4th and 2nd, sobresaut, temps leve and jete.
That's a lot, huh? Well, I also teach a basic class that is the foundation for all of that.
In an intermediate class, I want to see beats: royalles, entrechat quatres and trois, cabriole. Multiple turns as well as turns in second, arabesque, front and back attitude, and fouette pirouettes. They should be able to reverse and invert a petit allegro combination. Across the floor I want to know they can do saut de basque, tour jete, fouette arabesque, traveling fouette turns, multiple pique turns.
In an advanced class, it's no longer a matter of vocabulary (although there are indeed some steps that only very advanced dancers and pros attempt) as much as it is about speed and weight changes. At the barre, the weight is constantly shifted from one foot to the other, combinations are reversed and inverted, and turns are added to just about every exercise. Combinations are very speedy and lengthier. In the center, I expect the same, with fewer "in between" steps. E.g. petit allegro combinations without glissade. A pirouette will land in arabesque and then fouette into an en dehors attitude turn...in other words, steps will be combined in ways that challenge both the body and brain.
Keep in mind that many classes are combinations of beginner and intermediate or intermediate and advanced. I have heard of classes defined as "slow beginner" or "advanced beginner" and so on. There are simply many, many ways to characterize a class and they vary from instructor to instructor. Once you get to know how a teacher works, you can better understand her classifications.
Never judge a class by its title.
That being said, my Friday morning class will no longer be called "Intermediate/Advanced." Instead, it will be "Intermediate" and just about any of my current students will be able to handle the material. The speed will be only slightly increased and some of the combinations will be more of a challenge but I don't want any of my students to feel intimidated. Just come and enjoy.