Cats normally greet people or announce their presence using a short sound.
Lengthy meowing indicates that your cat is very glad to see you. This occurs if you are away from home for a long time.
A medium- length meow might be a request (for water or food).
A long "mirrrrrrrrrrrrr-meowwwwwww" is a more insistent request or demand.
A low meow is a complaint, indication of dissatisfaction, or a readiness to fight.
A loud low sound often indicates an urgent demand (e.g. food)
A purring or vibrating sound indicates a desire for closer contact or attention. Cats purr for various reasons, but most often they do it when they are happy.