What is the difference between Network Address Translation and Port
Address Translation, and which is used by SOHO routers.

Hello Bcaff05,

The comment is basically correct but omits some key information.

Network Address Translation (NAT) is used for "outbound" connections,
translating network messages on the private LAN to those that can go
to the internet. A computer on the private LAN can initiate
connections to the internet (and replies get through), but a computer
on the internet cannot initiate a connection to a computer on the
private LAN.

Search phrase:
  define:"network address translation"

Port Address Translation (PAT) is used for "inbound" connections,
routing internet messages for a specific address and port to a (or a
few) computer on the private LAN.  For example, if you have an "always
on" network connection and a SoHo firewall, you can set it up to route
http (web) accesses to a web server on the private LAN, and smtp
(email) accesses to an email server on the private LAN.

Search phrase:
  define:"port address translation"
returns no references (quite surprising to me) but
  "port address translation"
or
  explain "port address translation"
both provide several good references.

Please make a clarification request if you need a further explanation
of some part of the answer or if some part of the answer is unclear to
you.

  --Maniac

NAT is many to many while PAT is many to one

I think SOHO has both.