I don't want to say how your providers equipment works, but
in every modem/router that I have ever worked on the assigned IP is based on the MAC address of the equipment connecting.
If it's handing out internal network address's (ie 192.168.1.xxx) its may have 192.168.1.101 on a wired connection but will get 192.168.1.105 wirlessly.
This is still the same if your modem is handing out external public IPs.
The MAC ID's of your ethernet card and wirless card are different and from all normal networking protocols it should be impossible for your computer to have the same IP when connected via 2 different mediums.
Try connecting both ways, verify that you have an interconnection by going to google and do an IPCONFIG and verify your IP address.