Is a router also a modem?

I have a Linksys – Wireless-G Broadband Router with 4-Port Ethernet Switch
Model: WRT54G2 from bestbuy. I need to choose an ISP for my new apartment and I am thinking about comcast. when I try to sign up for comcast, they ask if I need to lease a modem for one person, purchase a gateway for up to 5 people or if i already own a modem. They also ask if I want installation on 1 computer or installation on 2–5 computers. So will my old router count as a modem? and which installation will I need to choose for me and my roomate? can I just get the installation on one computer and use the wireless router so my roomate can have internet?