Back in the old days, a candidate would send a department a list of references and the department would send to each reference by postal mail a request for a letter which would be sent back by postal mail and followed up by a thank you sent again by postal mail. Faculty had a lot more secretarial support back then. This year I only got one such request, from a math department. Many departments have the candidates ask the recommendors to send letters directly by post and/or email. The best organized departments send the recommendors a link that leads to a secure upload page that puts the letter directly in the department's database.
Some misguided people like to send letters by post because they worry about the security of email and the electronic storage of their letters. Letters sent by post are far less secure. Copies of these letters must be made and these copies get left, on copy machines, in mailboxes in public areas, on peoples desks and in conference rooms. In any case it doesn't make sense to go crazy over security, any student with a little imagination can find a way to see their letters. Students: Don't do this. No good will come out of it.
There is an old saying "If a price is advertised as under $30 you can rest assured it is not $19.99." I take this saying into account when I read recommendation letters, particularly lines like "among the top half of complexity theorists graduating this year". In general I read letters more for what is not said than what is said.
"Strong potential" looks good for a fresh Ph.D. and the kiss of death for a senior candidate.
I ignore negative recommendations as probably personal issues. If you really dislike someone write a lukewarm letter. Seriously, if you don't feel you can write a strong letter for someone make up an excuse for why they shouldn't list you as a reference. Don't refuse to write if you get a request directly from a department. No letter is seen as a negative letter.
"I recommend" is a weak recommendation. "I very strongly recommend" is a strong recommendation. "I give my strongest recommendation" is a meaningless lie. "Don't hire this person because we plan to make him/her an offer and we want him/her for ourselves" is as strong as they get.