Different computer but same public IP address?

Yes, this is most common. Your computers are going in and out from the same internet gateway.
There are 2 types of IP address; the private IP is issued locally by the local IT administrator. The public IP address is issued by your Internet company.  In many situations, your organization is using a dynamic IP address internet. The IP address is known as floating IP address which is not permanently attached to your organization. This IP address will change after a period of time known as leased period.
In order to be shared by many peoples in the organization, you have issued a private IP address. The private IP address communicates with the public IP address, to send and receive internet data. 

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