Bourne: if statement testing exit status

What is the difference:

if IsServerStarted ; then ...

and

if [ IsServerStarted -eq 0 ] ; then ...

Seems to me that these two statements should be equivalent? Strangely the second statement is always true.

The following runs the shell function or executable in $PATH named IsServerStarted, and if its exit code is 0 (i.e. true), runs the then branch. If such a function or executable does not exist, the exit code will be non-0 (i.e. false) and the then branch will be skipped.

if IsServerStarted ; then ...

The following has [ (aka test) check whether IsServerStarted is an integer equal to 0, which (IsServerStarted not even containing a single digit) is always false. Thus, [ exits with a non-0 (i.e. false) code and the then branch is always skipped.

if [ IsServerStarted -eq 0 ] ; then ...

Actually, the second one will give an error complaining that "IsServerStarted" is not a valid integer. It's considered a string constant so something like

var="IsServerStarted"
if [ IsServerStarted == "$var" ] ; then

would succeed (or fail if it wasn't equal).

ndim is correct regarding the executable or function in the first example you gave.

A couple more variations to consider:

if $IsServerStarted ; then ...

In that one, the if is evaluated based on the return value of a command (executable or function) that is contained in the variable IsServerStarted. So you could set IsServerStarted=true and then the if would succeed since true is a shell builtin that always returns true. You could set IsServerStarted='grep popsicle freezer' and theif` would pass or fail depending on whether you were out of treats.

if [ $IsServerStarted -eq 0 ]; then ...

This simply tests whether the variable is equal to zero. If it's not a valid integer it will cause an error message.