i first have a question about the difference between the modules Net::SMTP and Net::SMTPS, because it looks like both can do the job.

Yes, both can do the job now. This was not always the case - Net::SMTPS exists because Net::SMTP never used to have any TLS support. Since it does now you should be able to use either. I tend to stick with Net::SMTPS purely out of habit.

This is covered in the DESCRIPTION of Net::SMTPS as quoted verbatim by brother atcroft in his reply.