I'm looking for advice an suggestions about SSO for Kentico in a couple of cases:
1). 2 Seperate Kentico web sites hosted on the same server.
2). A kentico website on one server and an internal app on a second Linux server.
In both cases authentication should be private and not use an external third-party.
regarding 2 separate Kentico web sites. If you setup both sites on same instance (database) you can easily setup single login. Because users can be global and you can assign a site to them. We have used this once in scenario main site and partner site.
Any tips on configuring that so users won't have to login again when going between the two sites (which would be on seperate domains).
as long as your users are global and assigned to both sites:
If you are using register web part here is how to do it:
We did this few years ago. I would recommend that you test it out.
Here is some documentation on your question: https://docs.kentico.com/display/K82/Configuring+single+sign-on
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