You arent "sharing" an IP address on the same subnet, you are translating an IP address from one class to another, or if you are using VLSM, (variable length subnet masking) you translate from one subnet to another.
There is no "fake" ip address, typically NAT is used to translate from public IP address that are routable on the 'net to private IP address that are not routable on the 'net. Maybe this is what you mean.
What you just described is actually called PAT, Port address translation or NAT overload. PAT is a subset of NAT that uses random high port numbers within a Table to map traffic flows between the public IP address and the private ip address.
It is not correct to say that the system shares an IP address, because it doesnt, it has its own IP address. Rather the router translates and tracks traffic flows from the "internal" Systems to 1 IP address on the outside, to avoid a flaw in IPv4, naminly the amount of IP address you can have ie 2^32