I wished I had seen this thread earlier than today. I'm in IT for libraries and I can probably answer quite a few questions, but not necessarily to full accuracy for what a particular library or region is doing.
Dynix seemed to be the defacto standard for a long time in Alberta. I'm not entirely sure if everybody used it, but most libraries did. Dynix was the name of the program made by Dynix.
Sirsi and Dynix merged into SirsiDynix and they made new and improved products. Horizon and Symphony being two of the most commonly used ILS (Integrated Library System) software used in the province today the other is Polaris. The two large libraries, CPL and EPL (Edmonton), do a lot of their own in-house development to customize the way their staff and patrons interface with the ILS.
BiblioCommons is the online portal where you, that patrons, can manage your account and items checked out or holds you have placed. BiblioCommons has a huge market share for libraries.
As for the hardware that you used in the library back in the late 80s and early 90s? Probably WYSE terminals. In the late 90s windows computers were used, at least by library staff, and Dynix was a terminal window that connected to the server.
I was part of a team that integrated from Dynix to SirsiDynix's Symphony over a decade ago. What a HUGE job that was! Even though I wasn't an end user of Dynix I miss it because it is your typical early 90s style program that I grew up using.
https://en.wikipedia.org/wiki/Dynix_(software)