"Segregation" simply means keep separate; in the context of IEC 62304 it can have several effective meanings, even the standard uses it for different meanings in different places. In one place it is used for classification, in another (5.3.5), it has the double channel meaning, generally for high risk devices like a surgical laser or infant incubator.
The original question has the highest level meaning, which is in effect "what is a software system?"
IEC 62304 applies to the medical device, which is the object that is actually placed on the market. For each medical device which contains software, there should be at least one software system and hence one SRS.
The original question had four types of software related to the medical device. So we really need to ask first: is each one a medical device? The firmware seems to be yes, PC software and database maybe, and the production software seems to be no.
The next question is: are they sold as a package or as individual medical devices? If for example the device with the firmware, the PC software and/or the database are sold or placed on the market separately, then definitely you need individual SRSs to comply with regulations.
If they are sold as a package (single medical device), then it is flexible. In practice, if there are two or more processors (e.g. firmware, PC software), it makes a lot of sense to separate into individual SRSs. It gets too complicated otherwise. Of course, there should still be a "system specification" for the final medical device (hardware/software/mechanical etc) that ties everything together, including the interconnection of the two software systems. But that is out of the scope of IEC 62304.
The key point it to always have in mind the "medical device", and the work top down from there. If you have an SRS for the firmware, it should somehow fit within that framework.
For the production software, there is no requirement to control as a "software system" under IEC 62304. You only need to meet Clause 5.8.5 (document how software is released), there is no need for an SRS, risk management, configuration management etc etc.