It just took me a while to really understand the differences between this three. But hopefully (never say never ;-), now i got it.
A callback simple describes, that a function awaits another function as parameter. This functions can be an existing one or a "on the fly created on" with the power of create_function.
A lambda function is a function without a function name. The reference is stored in a variable. You can use this variable to handle it over to methods like usort.
As everybody i will use a sorting lambda function for showing what i mean.
A closure is a function that surrounds (i do not want to use the word enclose ;-)) the lambda function.
That has the sideeffect that the closure itself conserves their own context. An easy example is a simple logger.
$status = $myDatabaseInfoLogTable->save();
$myFileErrorLog = new ErrorLog();
$myFileErrorLog->addMessage(mktime() . "\t" . $message);
$status = $myFileErrorLog->save();
$infoLogger = myClosureLogger('info');
$errorLogger = myClosureLogger('error');
$infoLogger('This is a info log');
$errorLogger('This is an error log');
The positiv thing about closures is, that the code footprint can be reduced (you even can use closures inside objects - even as static if you do not need to access on the object itself with $this).
The negativ thing is, that you can not use interfaces which implies a lose of security.