A student apartment is a form of off-campus housing for college students. Student apartments typically are not owned by the college or university but are available to those who are enrolled in college classes and are generally priced for a per bed lease.
A dorm is located on a college campus and is usually small, while a student apartment is off-campus, which provides more privacy and is more spacious. Since dorms are on-campus, a college or university may have strict rules for dorm residents, such as curfew and frequent inspections.
Those living in student apartments are still subject to rules, but those are set by the landlord.
Dorms usually have a meal plan and on-site dining facilities, but in an apartment, you're on your own, so you better start learning how to cook. In fact, living in a student apartment means you'll be on your own in other ways, too, like in getting furniture.
Dorms will already have a bed, desk and even a dresser to use, but a student apartment may not have any of those things, so you'll have to buy them.
Based on what you're looking for, either could be a great option. One will give you more things provided to you, while the other will give you more independence and autonomy.
Everything depends on what you want. If you've lived the dorm life and want to move on to live a little more independently, a student apartment is probably the best choice for you and will give you more freedom.