How different is the use of waitforchild from this?

the Colon, : is used to call a function on an object, this is what we usualy refer to as a method. Methods have the self parameter in them automatically, which refers to the object the method is being called upon.

This is why WaitForChild(script,"Rocket") is doing the same thing as script:WaitForChild("Rocket") as script will be self when using the Method variant.

Eg.

function Thing:Rename(Name)
    self.Name = Name
end

would be the same as

function Rename(Thing,Name)
    Thing.Name = Name
end