No, it isn't. First code is declaration of closure, i.e. anonymous function. It has no name and can be called with identifier that holds it. Second sample is normal function (user-defined function, to be more specific) and, thus, it will be accessible within all scopes via it's name - not like closure, which will be available for calling only within scope, where it was defined.
You can have as many closures as you wish - they are just callable entities, for example this is valid:
$provider = function() { Code here }
$another = function() { Code here } //same code
-and calling $provider
(for example, with call_user_func()) will have nothing to do with $another
Another significant difference is that closure can accept context parameters like:
$provider = function() use ($param1, $param2, ...) { Code here }
-so inside it's body context parameters will be available. Context parameters are not like usual arguments - since context parameters defined and exist independent from closure while arguments are evaluated at the moment, when call happened.