The SSID is only part of the information used between an AP and a station, and many software clients will aggregate or simplify the networks they find into one entry in the wireless networks. However with most enterprise wireless solutions, each AP will have a separate BSSID (looks like a MAC address) that is associated with a logical interface on the physical interface.
With some software clients (Intel used to do this, but I haven't used it in a while so not sure if they still do), you will see each unique AP/BSSID listed in the wireless network list, so you end up with multiple entries with the same SSID. You can also use a software tool like InSSIDer to view the individual devices broadcasting the same SSID.
You are correct in that they share the same "collision domain" and resources, however there are many reasons to do so. For instance, you may want to provide different security mechanisms such as WPA2-Enterprise for your employees and an "Open" network with a captive portal for guests.
You could do this with two different sets of APs, each doing one or the other. However in the 2.4GHz space, you really only have three channels to work with in your channel plan, so unless you only need one AP for each, you are going to have channel overlap and still be sharing the "collision domain" (and this also complicates the channel planning significantly, but that's another discussion). Better to do so with multiple logical interfaces on one device as this means less devices, a lower cost (both capital and operational), and a simpler network to manage.
Now there is a caveat, and that is with each additional BSSID/SSID on a physical device, the more you do lower the efficiency of the RF use, mainly because you are creating additional management traffic in the air. While dated, you can find a good explanation on this effect in this document, if you are interested.