Hello oddmanout;
Sorry about your frustration, but...
If you can't find ANY answer on the web, and I guess the web is the greatest trove of dissiminated knowledge ever built... Maybe the original question is inadequate. Maybe that's the way it was written out in your manuals, but I can assure you that the dichotomy fixed/modular does not exist in the world of real, professional PLC programmers. Maybe you could go back to your teacher and ask for more explanations.
The names and distinctions between PLC types is more a matter of marketing by the manufacturers than a real naming convention.
Sometimes we will speak of "bricks", small PLC units that combine the processor and some inbuilt I/Os. Generally these are small-application oriented, small-memory PLCs: Siemens S7-200, Omron CFQ1, and others. But nowadays you can add I/O modules (digital and analog) and communication modules to these bricks to extend their range, so does that make them modular? I won't event attempt to answer that one.
Even the lowest usable Programmable relays (Siemens LOGO!, Moeller Easy, Rockwll Pico and others) come now with expansion modules of some kind, and their processing power is increasing, making the distinction between small PLC and Programmable relay less distinct than it was 5 years ago.
Sorry for the rambling, but just keep in mind that the peopo=le here will probably give you the best answer they can to a question that they can answer.
And your question has none, in our world.
Regards,
Daniel Chartier