In JSONP technique, server should wrap the response in javascript function. There is a clear explantion given on jsonp technique here:
jQuery's "dataType: 'jsonp'" will just make sure to add callback parameter to your url.
Just add a '&callback=func123' to both the URLs, twitter will respond you with wrapped data where as the other service is not.
twitter : URL
findschoolzones : URL
Its is server's responsibility to identify the callback parameter and returns a wrapped data.