Welcome to "compatibility". Your Linux box does not even have sendmail installed. It has exim, which is a perfectly fine email system that can pretend to be sendmail for many purposes. (This is another reason I always try to use Net::SMTP ... I *know* I'm always getting the same interface).

Further, it looks like your exim has configuration problems. Someone with root access needs to run eximconfig(8) and get it working properly before you have a chance to make your scripts work ...