Hostels (called "hostales" in Spain/Spanish - and not to be confused with YOUTH Hostels which are called "albergues juveniles") are typically privately owned/operated budget hotels in Spain where you'd have your own private room, your own key, and in many cases your own in-room bathroom as well. Hostels are usually very very simply furnished with only the bed(s), a small table for a lamp, and maybe a small desk and chair.

Apartments are typically larger, often has a separated bedroom (unless it's a studio apartment), and always has a private bathroom. Apartments are usually furnished with all the things you'd need to live including a kitchen, possibly a stereo, maybe a television, a sofa, chairs, dining table.

Saludos, MadridMan