\edef expands the argument, whereas \let doesn't. Here is an example to illustrate the difference:
\def\txt{a}
\def\foo{\txt}
\let\bar\foo
\bar -> a
\def\txt{b}
\bar -> b
However,
\def\txt{a}
\def\foo{\txt}
\edef\bar{\foo}
\bar -> a
\def\txt{b}
\bar -> a
There are also other differences, say, the arguments and so on. But how to expansion may be the most important(?).
This is an interesting question. May I expand the question further more?
What is the difference between \let and \expandafter\def\expandafter\foo\expandafter ? Do they always behave the same?
\def\txt{bar}
\def\foo{\txt}
\expandafter\def\expandafter\bar\expandafter{\foo}
\let\BAR\foo
{\tt \string\bar = \meaning\bar}\par
{\tt \string\BAR = \meaning\bar}
Sneaky inline answer to this rhetorical question, since I wrote the original question :)
If you are doing this on macros that take no arguments, then the difference between them is negligible. OTOH, you cannot use the \expandafter\def... construct if you're trying to copy the definition of a macro that takes arguments.
In fact, this brings to light one of the aspects that I was hoping people would discuss here. \let creates a literal copy of a macro at the instant that it is executed, whereas \edef will take the contents of the macro and expand it recursively to create a new macro entirely. When you are only using the macros as places to store data (such as \def\name{Will}) then the differences are largely inconsequential, but when the macros are being used as ‘functions’ that take arguments or have contents that have various expansion restrictions applied to it (with \protected, \noexpand, and so on) then the differences can be very important indeed.
The \tolerance setting influences the paragraph breaking routine itself: changes to \tolerance (and \pretolerance) actually affects which line breaks are chosen. Higher values allow worse lines (usually meaning: with stretched inter-word spaces) to be accepted, with the value 10000 indicating a 'panic mode' where anything at all is acceptable. Normally the lower the value, the better the paragraph will look, but you run the risk of reducing the list of possible breaks so much that you end up with overfull lines.
The \hbadness setting only influences the user report (the messages you see on screen and in the log) about the actually chosen lines, it has no effect on the breaking routine itself.
Best Answer
Here's in D. Knuth's words
Sample.tex
sample.log shows