Bash – SDERR and STDOUT File descriptors in a BASH script for logging

Avoid using /etc/mtab because it may be inconsistent.

Avoid piping mount because it needn't be that complicated.

Simply:

if grep -qs '/mnt/foo ' /proc/mounts; then
    echo "It's mounted."
else
    echo "It's not mounted."
fi

(The space after the /mnt/foo is to avoid matching e.g. /mnt/foo-bar.)

There are several differences. In my opinion, a few of the most important are:

1. [ is a builtin in Bash and many other modern shells. The builtin [ is similar to test with the additional requirement of a closing ]. The builtins [ and test imitate the functionality /bin/[ and /bin/test along with their limitations so that scripts would be backwards compatible. The original executables still exist mostly for POSIX compliance and backwards compatibility. Running the command type [ in Bash indicates that [ is interpreted as a builtin by default. (Note: which [ only looks for executables on the PATH and is equivalent to type -P [. You can execute type --help for details)
2. [[ is not as compatible, it won't necessarily work with whatever /bin/sh points to. So [[ is the more modern Bash / Zsh / Ksh option.
3. Because [[ is built into the shell and does not have legacy requirements, you don't need to worry about word splitting based on the IFS variable to mess up on variables that evaluate to a string with spaces. Therefore, you don't really need to put the variable in double quotes.

For the most part, the rest is just some nicer syntax. To see more differences, I recommend this link to an FAQ answer: What is the difference between test, [ and [[ ?. In fact, if you are serious about bash scripting, I recommend reading the entire wiki, including the FAQ, Pitfalls, and Guide. The test section from the guide section explains these differences as well, and why the author(s) think [[ is a better choice if you don't need to worry about being as portable. The main reasons are:

1. You don't have to worry about quoting the left-hand side of the test so that it actually gets read as a variable.
2. You don't have to escape less than and greater than < > with backslashes in order for them not to get evaluated as input redirection, which can really mess some stuff up by overwriting files. This again goes back to [[ being a builtin. If [ (test) is an external program the shell would have to make an exception in the way it evaluates < and > only if /bin/test is being called, which wouldn't really make sense.