Yes, "//" indicates that the rest of the line is a comment (or until it escapes out of PHP at a "?>" on that line). I just tested on my PC, and each of the following lines generates the same error:
<?php echo // "this is ignored by the parser" ?>
<?=// "this is ignored by the parser" ?>
What I think is happening is that the parser assumes a ";" when it gets to a closing "?>" if none was specified, but the comment after the "echo" means that the command is incomplete, thus the somewhat misleading error message. Since "<?=" is equivalent to "<? echo", you are seeing the same thing.
As to why you don't get the error on the other server, I do not know. Maybe a version difference, or some config option I don't know about? (Or maybe it's not commented on the other server?)