How should a numeric value that is an external key be stored?

This is something I was pondering recently. trying to determine how to store certain values. The best wide spread example I can think of is Federal Employee Identification Number - more commonly knows as tax id or social security for companies.

For various business / tax / legal reasons we need to store this number for some of our clients. Now this is a numeric 9 digit field . However it doesn't change. There are no calculations to be done with it, this is an external reference field that we have no control over. So should it be stored as char(9) or int(9) ? What are the benefits of storing one way or another? What's the most efficient way: in terms of space usage(I'm assuming int) , and in terms of performance ( speed of look ups) assuming that we will create a unique index on this column either way?

For the purpose of this exercise DB doesn't matter, but if want to elaborate I use MariaDB cluster ( MySQL)