Volume
Volume is a measure of how much space an item takes up. In Wurm the word 'volume' typically refers to numbers for capacity of containers, rather than taking up visual space or effecting movement.
In Wurm, volume is measured in liters (L), and used mostly to measure liquids and bulk storage. This is different from weight, which players become familiar with first, since the player inventory is based on weight.
Many containers accept liquids, and some accept solids or liquids. Those that accept liquids have their capacity measured by volume, including solid items placed inside. This can be deceptive, however, since the number displayed is still the weight and not the volume. Only in bulk bins does the "weight" column in the container window actually mean "volume".
For example: A small bucket can hold 16L of water, and those 16L weight 16kg in a player's inventory. If a solid items are placed in the bucket instead, and those items have different weight and volume per unit, the bucket may contain more or less than 16kg in a player's inventory when full. This difference is due to density.
Density
This is an advanced topic and not of great use to new players
Some items weigh more per volume than others. Density (weight per volume, kg/L) is useful for measuring how well items store in volumetric containers, especially bulk storage bins and food storage bins. Higher density means that for each kilogram, less capacity is consumed in the bulk bin.
For example: planks are more than twice as dense as logs, and woodscraps far more than that, so sawing a bulk bin full of logs will result in a bulk bin half-full of planks and woodscraps, even though the total weight remains the same.