Two very different platforms.
To make a very long technical story short,
They are two very different internal architectures with a fair number of differences….and yes they can be made to sorta work, but……..they only really appear to work, as some of their internal functionalities get messed up.
They are designed NOT to work reliably if installed in the incorrect MAC OS environment (Parallels Workstation on Mac Server vs. Parallels Server on Mac non server workstation)
The reason being that they are designed, created and coded, to work very reliably for two very different use cases.
For the Server Edition…..
For example, if you have a windows server, as in people inside a company are depending on a windows server for a specific function, typically something like the multi-user terminal server edition of QuickBooks Pro Enterprise which alone costs $5,000. Note QuickBooks Pro Enterprise (Windows Terminal Server Only) is now typically one of the largest use cases in the small - midsize business world, which is why, for many years many organizations could not consider the MAC platform.
Thanks to the Parallels Server Product, QuickBooks Pro Enterprise + Windows Server is now one of the largest small - midsize company uses of Parallels Server for Mac Min edition.
So anyway, you have virtualized the windows server and then placed it on a Mac Mini Server, that Server MUST be up at all times to provide the windows server services to support accounting, in this example, on that combination windows and accounting platform.
To accomplish that end, the Parallels Server for the Mac Mini loads as a service, along with all manner of additional server support interfaces / services rather early (Mac Workstation edition does not), along with multi virtual server management tools / interface (very different than workstation edition), in the booting process.
Thus even if the Mac Mini Server comes up and no one is logged into it at the console or remotely, as a traditional Apple centric MAC user, Parallels is already up, the tools have loaded the slightly modified windows server, and then the virtual MS Windows server is up and ready and loaded so it can be multi user accessed over the network independently of the MAC OS environment on that mini server.
Also note that the server edition is designed to deal with the hardware and software resource contention of running two fully simultaneous server grade OS virtual machines, fully functioning, at all times, while also allowing access to the Mac Min Server full Mac server OS (more features than the MAC workstation) and processes functionality.
For the Workstation Edition……
The use case for the workstation, is that you will boot up your mac, log into it, then launch your Parallels Workstation to load your windows or linux "PC"….and the internal infrastructure to support multiple simultaneous users and resource contention at the server scale is just not there.
Note that you can run server grade OS as guests inside workstation on a workstation, but it will "Choke up" rather quickly under any significant true multi-user load.
Also note that there are plenty of differences to support all the internal plumbing for real - time multiple simultaneous user access through the Mac Min Server into the virtualized server (supports at least two) living inside the Parallels Server for the Mac Mini.
You might want to consider…..
If you are new to virtualization, and are in IT, as a career, and you are not fully familiar with server grade virtualization, spending the additional money to buy the Parallels server version may be the "gateway" for you into professionally growing into the real world of virtualization and cloud computing.
Getting the experience with the management tools, as well as the ability to run and manage all manner of server OS virtual applications, as a server virtualization administrator, and not a workstation user, will help you start to learn the basics of data center scale server grade virtualization. It is a great foundation that then you can extend into the larger universe of Parallels Hosting Virtualization Products, and or competing platforms like Xen, Microsoft or VMware based virtualization / cloud technologies.
We are Parallels Partners and Cloud Architects, so our suggestion is taken from the experience of teaching associates.