The term "youth" is less often used with these properties. These non-HI hostels are often called "backpackers' hostels". Unlike a hotel chain where everything is standardised, these hostels can be very diverse, typically not requiring a membership card.
There are chains of independent hostels throughout the world such as the Jazz Hostels on the East Coast and Banana Bungalow Hostels on the West Coast of the United States, or the Generator Hostels and Equity Point Hostels of Europe, or Zostel of India.
Each offers their own niche of services to travellers and backpackers. For example, one independent hostel might feature a lot of in house gatherings, another might feature daily and nightly tours or events in the surrounding city, and another might have a quieter place to relax in serenity, or be located on the beach. This is an independent hostel's personality and travellers will frequent the hostels that offer the personality that they find desirable. There is frequently a distinction being a "party hostel" or not.