Low density memory has more chips on the stick maybe 8 per side. The chips themselves are for example 16MB. When multiplied by the number of chips on the stick the result is 256MB ram. The high density sticks may only have 8 chips to make up the 256MB because the chips are 32MB.
This usually isn't always true. High density modules can have 16 chips (8 on each side). 'Standard' RAM chips are organized a DEPTH x 8 Bits. E.g. 32x8, 64x8, etc. That means 8 of the chips make up a 64 bit wide rank (memory bus is 64 bits wide). "Double Sided" is an old term to describe a stick with 16 chips, 8 on each side. And with DEPTH x 8 chips that makes for 2 ranks (or, again in an older style terminology: 2 'banks').
'High Density' chips are DEPTH x 4 bits so it takes 16 to make a 64 bit wide memory rank. And this is why "double sided" is no longer the favored description because when x8 chips are used "Double sided" means "double rank" but with x4 chips it takes both sides and 16 chips to make the ONE, single, rank.
Now to the problem. A memory 'slot' is usually designed for 'standard' x8 chips and memory sticks containing 2 ranks. That is how the 'capacity' will be described. I.E. the SY-6VBA says it can handle up to "1.25GB" with four slots, and that means a possible combination of 2x 2 rank modules and 1 single rank module never exceeding 256MB per rank. You could probably cannot use 512MB in each slot. It has to do with the configuration of the MB chipset.
But a 'high density' memory stick crams the 512MB into ONE RANK by using 16 deeper (twice as deep) x4 bit width chips. And this is how they arrive at the confusing term 'high density'. The chips themselves are no higher in density than the x8 chips but since they are organized as x4 they can cram more 'bytes' into a single rank because 16 chips make up a rank rather than 8, not that it helps make the stick itself any 'higher' in 'density' because you can still only get 16 chips mounted on the thing.
So, a 512MB 'high density' stick puts 512MB in ONE RANK and a 'standard' (low) density 512MB stick is two 256MB Ranks. Same size, same 'density'. It's the RANK organization that's different.
Conclusion, I always look at the max amount of memory the MB can handle. If it cannot accept more than 1.5GB of memory, than it will not accept high density memory. (normally the manufacturer of the MB will state the max memory in the description)