When a user installs Sibelius 7, the software generates a unique System ID, which is a digital fingerprint of the computer's hardware and software configuration. The System ID is used to identify the computer and ensure that the software is not installed on multiple machines. The Activation ID, on the other hand, is a code that unlocks the software, allowing users to access all its features. The Activation ID is tied to the System ID, making it difficult to transfer the software to a different computer.