What is the difference between "prefix-casting" (Type)variable - and "as-casting" (variable as Type)?

Prefix-casting is usually quite a bit safer because if you run into an exception, it gives you a TypeCastException telling you exactly what's going on. As-casting on the other hand will simply return null if that cast is not allowed. This creates a couple of difficulties when there is a problem: a) you don't know if myVariable was null or of the wrong type, b) newVariable might be null and this might give you a NullReferenceException at a later point in time ... which might make debugging harder.

However, as-casting has one significant advantage: It's much faster. In most cases, this "much faster" won't matter much, but if you're on the iPhone or Android, or when you're doing those casts thousands of times per frame, it may make a difference.

In both cases, it's good practice to add some checks or exception handling; depending on what your exact needs are:

if (myVariable is MyType) {
    MyType newVariable = (MyType) myVariable;
    // ... do whatever you wanna do with newVariable
}

Or

try {
    MyType newVariable = (MyType) myVariable;
    // ... do whatever you wanna do with newVariable
} catch (InvalidCastException exc) {
    // do whatever needs to be done if that exception occurs
}

Or

if (myVariable is MyType) {
    MyType newVariable = myVariable as MyType;
    // ... do whatever you wanna do with newVariable
}

Or

MyType newVariable = myVariable as MyType;
if (newVariable != null) {
    // ... do whatever you wanna do with newVariable
} else {
    // ignore or send a warning or whatever you need to
    // do when either myVariable is null or not of the
    // correct type
}

In any case, it helps when you understand exactly what you're doing ;-)

Another difference I noticed: (Unity 3.5, C#)

//data is an arrayList with some Vector3's and other types stored in it. Vector3 spawn = data[0] as Vector3; //THIS FAILS Vector3 spawn = (Vector3)data[0]; // THIS WORKS