"the router noticed you were trying to reach outside the network, to a
resource inside the network, and replaced your IP address with the
gateway address"?
That is a NAT (Network Address Translation) variant called NAPT (Network Address Port Translation). Some people call it PAT (Port Address Translation) because a large vendor calls it that, But RFC 2663, IP Network Address Translator (NAT) Terminology and Considerations explains it. When you want it to loopback inside, that is called various things, depending on the vendor (hairpin routing, NAT reflection, etc.), and it is very wasteful of router resources.
There are various resources, including RFCs. For example, RFC 3022, Traditional IP Network Address Translator (Traditional NAT) has Section 2.2. Overview of NAPT:
2.2. Overview of NAPT
Say, an organization has a private IP network and a WAN link to a
service provider. The private network's stub router is assigned a
globally valid address on the WAN link and the remaining nodes in the
organization have IP addresses that have only local significance. In
such a case, nodes on the private network could be allowed
simultaneous access to the external network, using the single
registered IP address with the aid of NAPT. NAPT would allow mapping
of tuples of the type (local IP addresses, local TU port number) to
tuples of the type (registered IP address, assigned TU port number).
This model fits the requirements of most Small Office Home Office
(SOHO) groups to access external network using a single service
provider assigned IP address. This model could be extended to allow
inbound access by statically mapping a local node per each service TU
port of the registered IP address.
In the example of figure 3 below, stub A internally uses class A
address block 10.0.0.0/8. The stub router's WAN interface is assigned
an IP address 138.76.28.4 by the service provider.
\ | /
+-----------------------+
|Service Provider Router|
+-----------------------+
WAN |
|
Stub A .............|....
|
^{s=138.76.28.4,sport=1024, | v{s=138.76.29.7, sport = 23,
^ d=138.76.29.7,dport=23} | v d=138.76.28.4, dport = 1024}
+------------------+
|Stub Router w/NAPT|
+------------------+
|
| LAN
--------------------------------------------
| ^{s=10.0.0.10,sport=3017, | v{s=138.76.29.7, sport=23,
| ^ d=138.76.29.7,dport=23} | v d=10.0.0.10, dport=3017}
| |
+--+ +--+ +--+
|--| |--| |--|
/____\ /____\ /____\
10.0.0.1 10.0.0.2 ..... 10.0.0.10
Figure 3: Network Address Port Translation (NAPT) Operation
When stub A host 10.0.0.10 sends a telnet packet to host 138.76.29.7,
it uses the globally unique address 138.76.29.7 as destination, and
sends the packet to it's primary router. The stub router has a static
route for the subnet 138.76.0.0/16 so the packet is forwarded to the
WAN-link. However, NAPT translates the tuple of source address
10.0.0.10 and source TCP port 3017 in the IP and TCP headers into the globally unique 138.76.28.4 and a uniquely assigned TCP port, say
1024, before the packet is forwarded. Packets on the return path go
through similar address and TCP port translations for the target IP
address and target TCP port. Once again, notice that this requires no
changes to hosts or routers. The translation is completely
transparent.
In this setup, only TCP/UDP sessions are allowed and must originate
from the local network. However, there are services such as DNS that
demand inbound access. There may be other services for which an
organization wishes to allow inbound session access. It is possible
to statically configure a well known TU port service [RFC 1700] on the
stub router to be directed to a specific node in the private network.
In addition to TCP/UDP sessions, ICMP messages, with the exception of
REDIRECT message type may also be monitored by NAPT router. ICMP
query type packets are translated similar to that of TCP/UDP packets,
in that the identifier field in ICMP message header will be uniquely
mapped to a query identifier of the registered IP address. The
identifier field in ICMP query messages is set by Query sender and
returned unchanged in response message from the Query responder. So,
the tuple of (Local IP address, local ICMP query identifier) is mapped
to a tuple of (registered IP address, assigned ICMP query Identifier)
by the NAPT router to uniquely identify ICMP queries of all types from
any of the local hosts. Modifications to ICMP error messages are
discussed in a later section, as that involves modifications to ICMP
payload as well as the IP and ICMP headers.
In NAPT setup, where the registered IP address is the same as the IP
address of the stub router WAN interface, the router has to be sure to
make distinction between TCP, UDP or ICMP query sessions originated
from itself versus those originated from the nodes on local network.
All inbound sessions (including TCP, UDP and ICMP query sessions) are
assumed to be directed to the NAT router as the end node, unless the
target service port is statically mapped to a different node in the
local network.
Sessions other than TCP, UDP and ICMP query type are simply not
permitted from local nodes, serviced by a NAPT router.
The proper way is to use something like split DNS so that your internal traffic never enters the router, so that you do not waste the LAN interface bandwidth (in both directions), and you do not use router CPU and RAM for traffic that should never leave your network.
