The SMTP wiki article says SMTP typically uses port 25, however on my forum it's set to use port 26.  Is that something I should change, or is port 26 something specific to IPS?

https://en.wikipedia.org/wiki/Simple_Mail_Transfer_Protocol

If it’s working, it’s something specific to your server. 

I'm not sure it is.  It may have gotten changed accidentally.
We've been having trouble with our host where our search index crashes weekly for about... 8 months now.
We've tried everything to fix this issue, but our hosts tech support has been ineffective.
The one thing we still do run through the host is the SMTP, so I was trying to remove it to minimize the number of variables on the hosts end.
I mean php is an option, and it worked fine for us for a while.  It stopped working randomly when our site did a grand-reopening thing that lead to a registration spike, but also marked the beginning of problems with the email.  Now that I think of it tho, if that port number got changed while I was preparing for the reopening, that Could explain it..

Sorry for the ramble, it's just the context is long standing.

Wait a sec, Mark?  Was it you that was just helping me with that trouble ticket? lol

What Mark means is that, while Port 25 is the typical port used for SMTP, that may not always be the case. Any port can be configured for a particular service (Secure HTTP connection do not have to run on port 443, for instance).

So, if it is set to Port 26, and emails are sending properly, then that is the correct port to use for your SMTP server.

I understand that, but thank you for clarifying none the less.  What I'm wondering is precisely:
Where it does work on port 26, is it possible that it might also work on 25, and most importantly would I do any damage by testing that out?

That also depends on your server, although if both work, then you will not likely see a difference either way.

You can test it, yes - when you change the email settings, a test email is sent immediately which tells you whether or not the configuration works.