First-class passengers might have a seat that turns into a bed or even their own private apartment. Business-class might offer more legroom but doesn't offer a private space. The food and drink in business class are typically at a restaurant level.
Do low cost airlines have first-class?
Budget airlines tend to have little or no premium cabin seating, though this isn't always true. These days, some budget airlines will have options to upgrade to larger seats closer to the front of the plane or priority boarding access, but even then the perks are more along the lines of premium economy.