I think this might belong better in the Professional Brewing sub forum...
I have been doing extensive reading on the basic equipment in commercially breweries but have got all tied up and confused (too much knowledge may not be dangerous but certainly does lead to less clarity in my case!).
The main thing to understand is that systems are designed according to the needs of the brewery. There are many systems that are more like very large homebrew two vessel systems and some that are super sophisticated, computer controlled, multi-brewhouse plants that do extraordinary things to create wort. It's like vehicles on the road; all move, just how efficiently, comfortably and stylishly and what they're designed for is different.
What is the major difference, operationally and/or structurally (i mean paddles, shape, heating facility run off false bottom plates, grain cutting rakes etc) between a
mash conversion vessel
You forgot the term "mash cooker."
The main difference is the name and whether it's a dedicated vessel or a combi-vessel. "MLT" means "Mash/Lauter Tun" and is the only implied combi-vessel in your list however, the others might be the same depending on context and design. It may or may not have rakes or a mixing blade. Mine has a mixing blade, no rakes.
As dedicated vessels, the other four would be set up with a mixing blade near the bottom of the tank that stirs the mash upwards and past the steam jacket. These are only dedicated to mixing water with the grain and sending it through temperature steps. There might be two other associated mash tanks (one or both) for decoction or for cereal cooking. Again, it depends on the needs of the brewery. Since the 80's, decoction tanks have become increasingly rare, replaced with multi function cereal cookers, if needed at all.
In all dedicated vessels, the mash is pumped out to the lauter tun.
Since mash tuns (tanks) are frequently used for the run off (of wort) are they constructed differently?
When the mash is pumped out to be run off from a dedicated lauter tun are they in that case constructed differently (for eg no false bottom) as they will be ONLY used for single step or multistep infusion mashing and not for the run-off?
In short, yes. Ideally, mash tuns are taller and have a slimmer diameter than the lauter tun because the main goal is smooth heat transfer into the mash. A properly designed lauter tun will provide a wide, shallow grain bed that allows water through the whole thing without compaction or channeling. Rakes help smooth the grain and keep water flow even through it.
Since (sweet) wort may be lautered from a mash tun, how do such mash tuns differ from an MLT
Combi vessels will make compromises between both processes. Here, "compromise" is not a bad thing. Most of the time, a MLT is built with lautering in mind moreso than mash temperature steps. There is typically no change in conversion or extraction efficiency in a wide, shallow MLT and a dedicated vessel. Taller, deeper bed MLT's can experience some efficiency issues which have to be mitigated by brewer technique.
The main difference between combi and dedicated vessel systems is brew time and volume throughput. Properly planned, the brewhouse will match the volume, variety, and sales of the company. A four vessel 15 bbl system might actually be less productive and cost efficient than a well designed 30 barrel two vessel brewhouse. The choice might come down to variety desired by the company. The smaller brewhouse can crank out more brands in a day, but if there is one or two heavy hitters, the larger, simpler brewhouse will kill it.
With four vessel brewhouses, there is no major advantage until you get to larger scale and need to make 3 to 8 batches per day, nearly every day. Better beer is made through technique, not technology.