Grep knows nothing it does not see. If grep sees $string$, it will try to match $string{end-of-line}. What happens is that the shell expands the variable $string before grep kicks in, so that grep receives
test$ as the regex.
But, given the word $string$, why is the last $ is not expanded while
$string is? Because $ is not a valid variable name. This is very clear
in the POSIX specification:
If the parameter is not enclosed in braces, and is a name,
the expansion shall use the longest valid name (see XBD Name),
whether or not the variable represented by that name exists.
And XBD name states
In the shell command language, a word consisting solely of underscores,
digits, and alphabetics from the portable character set.
The first character of a name is not a digit.
And there are also special parameters, such as $$, $@, $#, etc..
If you don't want to remember all this, simply follow Gordon Davisson's advice
and escape every $ that should not introduce a variable to ensure it will
be preserved.
$ echo "$string$"
test$
$ echo "$string\$"
test$
$ echo "\$string\$"
$string$
Also remember variables are expanded in double-quotes but not in single quotes.
$ echo 'test' | grep '$string$' # No match, $string is not expanded
$ echo 'test' | grep "$string$" # Match, $string is expanded
test
I want to grep for a variable that has the string test, but I also want to make sure that it will only find test if that is the only word on a line.
For that, you need either the regex ^test$ (to anchor the string both to the start and end of line) or to use the -x flag of grep. Your original attempt would match Atest because the regex test$ is not anchored to the start of line.
$ echo Atest | grep "$string$"
Atest
$ echo Atest | grep -x "$string"
$ echo Atest | grep "^$string$"
