ok, I will try
pppoe provides you with encrypted tunnels from each client to a central server. it's an authentication method.
hotspot will force the user to log into a webpage form, before any webbrowsing will work. it's also an authentication method, but not encrypted.
mpls is a way to separate traffic and direct it through other ways, it's an alternative to routing, it assigns flags to packets
QOS means "quality of service" and means any method that improves the service quality
maybe it means giving each user his own connection speed, making sure others don't take away his bandwidth. maybe it means a lot more.