(note: parts of this post will be Intel-centric, I don't follow AMD platforms)
PC memory is divided into "ranks". A rank is a group of 8 chips (9 for ECC) that cover the complete width of the memory bus.
Normal desktop memory is "unbuffered" and this limits the ammount of memory chips that can be connected to a memory channel. You can have up to two ranks on a module and up to two modules on a channel. "Buffered ECC" server memory can go to higher rank counts but you pay for it in both performance and pricetag, and it's only supported on the higher-end server platforms.
Then there is the size of the chips themselves. In general newer platforms support bigger chips. The first DDR3 platforms only supported 2 gigabit chips (leading to 4 gigabyte dual-rank modules). Later DDR3 platforms* support 4 gigabit chips (leading to 8 gigabyte dual-rank modules). DDR4 platforms generally support 8 gigabit chips (leading to 16 gigabyte dual-rank modules).
Then there are space constraints. Laptops will usually only have one slot per channel, the same is true of some small form factor or bargin basement desktop boards.
Then there is the fact that vendors don't always tell the whole truth. There are many systems where the advertised maximum ram is based on 4 gigabyte modules but where 8 gigabyte modules do in-fact work.
Then there is the fact that the high-end desktop platforms (LGA1366, LGA2011, LGA2011-3) have more memory channels than the mainstream desktop platforms. The high-end desktop stuff also moved to DDR4 sooner.
Put all of this together and you end up with a wide range of advertised maximum memory.
* Sandy bridge and later officially, unofficially also X58 LGA1366
I understand now, basically the newer and pricier motherboards have higher quality (if that is a good way to put it) memory controllers, so that's why they can support larger quantities of RAM, it would also prefer to handle sticks of RAM with smaller quantities of memory, rather than the sticks that hold a larger amount of memory. – Cas – 2015-10-14T04:22:44.860
They have 'bigger' ones, and may possibly handle ram types that trade off speed for quantity, yes. – Journeyman Geek – 2015-10-14T04:25:59.740
1Motherboards have not had memory controllers for years. The memory controller is part of the CPU nowadays. – plugwash – 2017-03-16T21:21:14.067
But there's still one and the capabilities of that controller determine what sort of ram is in use. I intentionally left the location of the memory controller vague since it dosen't quite matter – Journeyman Geek – 2017-03-16T23:58:15.827