The IMSI is the international unique identity of the subscriber. That?s its
function.

The MSISDN is just the number that you must dial in your phone to access a
certain service of one subscriber (the typical is telephony). It?s not
usual, but one subscriber can have different MSISDNs for each kind of
teleservice (e.g. one MSISDN for telephone service, another one for fax
service, another one SMS, etc...). In the MSC/VLR this is called
multinumbering.

Imagine the IMSI as your ID card in the GSM network, and the MSISDN as your
postal direction: it can be changed, and you can receive letters of people
who really don?t know you, they just know a number to contact with you which
it?s not the same as knowing the data of your ID card.

Regards,