Hi Jeff
Horde, Squirrel & NeoMail all work exactly the same, but Horde seems to be a bit more feature rich. Whatever we have here is the latest version since it 'ships' with Red Hat O/S and we keep up to date on that DAILY. I can not tell you why one would show mail and another one not since there is no 'picking up' mail as you are familiar with POP3. These applications don't move mail from the server so all have access to whatever mail that account has.
When I have to use webmail I prefer Horde, but webmail can rapidly become a royal pain - and eat up disk space since unless someone actually deletes messages AND empties their trash, the mail just builds up on the server. Since there is no "delete all" function, (I dont think there is), you can only delete a screenful of messages at a time.
Personally, if I were providing email accounts to a community of users, I would not give them POP3 settings, forcing all but the most determined to use webmail. With POP3 you risk someone spamming out of your domain. This not only could cause every other domain on the server to suffer being blacklisted right along with you, but would cost you, and us, financially.
Chuckle... I know members of the tech team and the tech volunteers have slacked off responding in here, but it does seem a lot of folks log on to read but never post. The forums average about 32,000 hits a month so you would think we'd get more posts. Though no posts also tells just how well things are going with our servers and service!

Peace
Wolf