How can you have two different Turing Machine Numbers for the same Turing Machine?

Actually, you can have an infinite number of different Turing Machine Numbers for the same Turing Machine!

If you had already read the page that answered the question How do I figure out the Turing Machine Number?, then you can understand how that can happen. You can generate a different Turing Machine Number anytime you precede any machine "instruction" (also called Transition Function) with one or more leading zeros.

More specifically, if you look at Step 4 of the procedure on that web page, it says that you can optionally remove any leading zeros from the strings of 0's and 1's that were converted from "instructions". If you don't remove the leading zeros, you'll just get a bigger Turing Machine Number, but it still translates back into the same Turing Machine.

Even more so, you can insert some extra leading zeros to any such string of numbers, and that will give you an even bigger Turing Machine Number, but it too will translate back into the same Turing Machine.

Theoretically, since you can insert an unlimited number of leading zeros to any or every such string, you can see how an infinite number of different Turing Machine Numbers can be generated, and they all translate back to the same Turing Machine.