What is the difference between these AES encryption methods
I can immediately think of four reasons:


They're both not using AES256.  I see in the Obj-C document a direct statement that they are using AES256 (unless you deliberately change it), I don't see any statement in the Visual Basic document that says what key size they're using (unless that's what they mean by "Block Bits").
Different keys.  AES256 takes a key of 256 bits; there's no standard method to take a five character string and convert that into a 256 bit value.  Now, there are a lot of possible methods; there's no particular assurance that they both use the same one.
Different modes of operation.  The AES block cipher takes 128-bit values, and translates that into 128-bit values.  However, not all our messages can fit into 128 bits, and in addition, sometimes there are other things we'd like to do other than message encryption.  A Mode of Operation is a method that takes a block cipher, and uses it as a tool to perform some more generally useful function (such as encrypting a much longer message).  There are a number of standard modes of operations, the Obj-C document states that it is using CBC mode; the Visual Basic document has scary sounding words which might be a garbled explination of CBC mode.
IVs.  Some modes of operation (such as CBC mode) have the encryptor select an "Initialization Vector" randomly; that can be translated along with the encrypted message (because the decryptor will need that value).  One of the things that this Initialization Vector does if you encrypt the message a second time, the second ciphertext will not resemble the first ciphertext at all; that way, someone listening will not be able to deduce that you've just repeated a message.  The Obj-C document specifically says that it will pick a random IV (unless to tell give it one yourself).


As you can see, there are a bunch of reasons why the two ciphertexts may be different.  One thing you can try: hand the ciphertext from one to the other, and ask them to decrypt it; if they can, you can be pretty sure that both sides are doing basically the same thing.

One final warning: the visual basic document has some fairly egregious mistatements in it; either the author doesn't really know what he's talking about, or he is quite bad at explaining things.  I fear it may be the former; I personally would not trust any encryption software written by him.