[latexrefman] but it does log the redefinition in the transcript file

[Karl Berry]

    English version every occurrence of « transcript file » by « log file

Of course the "transcript file" and the "log file" are the same thing,
that is, there is only one .log file.

But it would not be good to blindly replace "transcript file" with "log
file". If you look at the occurrences, you will see why. 
("log <whatever> into the log file" would sound weird.)

The terms can be, and are, used interchangeably. I guess this should be
stated explicitly in the "@item .log" where it is first brought up.

At any rate, it's important to mention "transcript file" somewhere,
since that is the term that (La)TeX actually uses in the output. I mean,
as in:
  Transcript written on hello.log.

It's really too bad that one of the OS's at the time of TeX developed
reserved the extension ".log", or Knuth could have just used "Log file"
everywhere instead of the endless circumlotion. Oh well. -k