The maximum memory is often for all banks of memory being fitted. That would be 4 slots worth of memory so 4 x 8GB, the fact that laptops often only have 2 slots is irrelevant.
To explain; the processor will have 2 banks of memory and allow two DIMMs to be on that bank. They will then use a "chip select" line to select a DIMM within the bank. This allows them to cut down on the number of address lines coming out of the processor while still allowing the use of more memory.
If your laptop had 4 DIMM slots I would expect your 32GB to work as 4x8GB, but not necessarily 2x16GB as there may not be enough address lines going to the DIMM slots.
To clarify, what this means for a processor claiming to support 32GB (for example an Ivy Bridge CPU) is that it is most likely to only support 8GB DIMMs. This give the CPU its max RAM of 32GB in 4 DIMMS, and it is not likely to be able to support 16GB DIMMs.
From Wikipedia:DDR3
The DDR3 standard permits DRAM chip capacities of up to 8 gibibits, and up to 4 ranks of 64 bits each for a total maximum of 16 GiB per DDR3 DIMM. Because of a hardware limitation not fixed until Ivy Bridge-E in 2013, most older Intel CPUs only support up to 4 gibibit chips for 8 GiB DIMMs
That citation carries on to say that AMD supports 16GB DDR3 DIMMs just fine.
A newer CPU, such as a Haswell or later, CPU would definitely be able to support 16GB DIMMs (4 x 16 = 64).
UPDATE - this explanation came from the vendor:
The main problem is that the MRC (memory reference code) - which is part of the BIOS - does not support modules based on 8 Gigabit DRAM components (16GB modules consist of 8Gb components).
The MRC code reads out the memory-modules SPD-settings and finds that this module is using DRAM-chips with 8Gb capacity. Next it tries to look up the settings for the memory-controller in a table, but can not find any entries for 8Gb chips in the table.
As a result, it crashes.
If the MRC-software was modified - which nobody seems able to as the code is Intel proprietary and difficult to understand - your Ivybridge eventually might boot.
The next hurdle is a hardware limitation inside the CPU (can't get past first hurdle so this second hurdle is theoretical). Intel has said the hardware is missing in Ivybridge as well as most Haswells. Support for 16GB per module begins with 5th generation CPUs (broadwell).
Best Answer
Ram form factors are standardized, though typically there's two common standards per ram standard - SODIMM for laptops and small form factor systems, and regular ram.
Looking up the model numbers they're both SODIMM, though the former is 'regular' ram while the second one is low voltage ram, and premium branded (They slap a heat spreader on this).
My reasonably educated guess is that the Product and Item Dimensions are for shipping and are the size of the packaging. The regular ram probably comes in a clamshell, and the other ram comes in a box. Looking up both models confirms they are SODIMM.
That said, one of these ram types is incorrect depending on the system. Some systems will only work with low voltage ram. Mixing low and high voltage ram may work if the system supports it, though the low voltage ram will be running at a higher voltage, negating many of the advantages of it.
A good rule of thumb is to try to match the ram you have.