Typically, where I live, forestry professionals use solid cubic meter of wood as the primary measurement. But, let's define all of the measurements. In this answer, I use the metric ton (1000 kg) as the definition of 1 tonne.
Loose cubic meter of wood is the amount of wood that will fill a container of 1 cubic meter, if the wood is thrown there in random orientations. Approximately 2.5 loose cubic meters is one solid cubic meter.
Stack cubic meter of wood is the amount of wood that will fill a container of 1 cubic meter, if the wood is stacked in the same orientation always. Approximately 1.49 stack cubic meters of wood is one solid cubic meter.
Solid cubic meter of wood is the true volume of wood. This volume is used as the basis in density calculations. So, if you know the density (based on the species of wood) and the volume, and want to know the mass, you must convert the volume into solid cubic meter first.
Note, that if you have 1 solid cubic meter of wood (growing stock), not all of it is sawlogs. Therefore, you can expect to ship perhaps half of it to a sawmill (assuming the forest has reached its renewal age; if you take wood from a very young forest, much less than half of growing stock is sawlogs), whereas the rest will be used for paper, pulp and energy industries.
Note also that the sawmill won't make 1 solid cubic meter of sawlog into 1 solid cubic meter of final product. 1 solid cubic meter of final products made by a sawmill may very well require as much as 2.3 solid cubic meters of sawlog. If you have a forest that has 50% sawlog and 50% pulpwood, 1 solid cubic meter of final products made by a sawmill requires about 4.6 solid cubic meters of growing stock (of which the wood that won't make it to the final sawmill products will be used by the pulp, paper and energy industries).
Tonne of wood is the weight of wood. Note the weight contains the weight of water in the wood, so if you dry some wood, the volume of the wood stays relatively unchanged, whereas the mass of the wood reduces due to evaporation of water.
Because weight of wood depends on the amount of water in the wood, forestry professionals prefer volume as the primary measurement. Mass is something that can vary, volume stays relatively unchanged.
For dry wood (humidity 20%), the following very approximate densities apply (I'm not listing densities of all tree species, as there are so many of them):
- Birch: 610 kg / solid m3
- Pine: 490 kg / solid m3
- Spruce: 480 kg / solid m3
If you see the density of wood somewhere, you must use it with caution: different values may be measured at different humidity levels. So, saying "1 tonne of wood" is ill-defined.
Some of the mass of wood is hydrogen atoms (either in water molecules or in some other form), some is oxygen atoms (either in water molecules or in some other form), some is carbon atoms, some is other types of atoms. So, if you have one tonne of wood, it doesn't contain one tonne of carbon sequestered from the atmosphere.
The amount of carbon dioxide one solid cubic meter of wood sequesters may vary based on the species, but the figures I have seen are very roughly 1 solid cubic meter of wood = 1 tonne of carbon dioxide sequestered for the typical tree species encountered in boreal taiga forests (spruce, pine).
Because carbon dioxide is 27.289% carbon, it's possible to do the following very approximate conversion: 1 solid cubic meter of wood = 0.27 tonnes of carbon.
Further complicating the matter is that some of the carbon sequestered is in biomass that is not commercially exploitable (and thus not included in growing stock figures). So, if you have one hectare of land, and grow 100 solid cubic meters of forest (growing stock) on it, it may very well sequester more than 100 tonnes of carbon dioxide from the atmosphere, because part of the biomass is underground and not included in growing stock figures.
If you're planning to burn the wood, you are interested in its energy content. The problem here is that wood contains water, so well-dried wood burns at a higher energy content than wood that hasn't been well-dried. The energy content of wood is about 14000 - 15000 MJ / tonne of dry wood (humidity 20%). Note if the wood is not dry, you cannot use the conversion.
Note, that 1 tonne of wood typical in boreal taiga forests (spruce, pine) is about 2.06 solid square meters of wood, sequestering about 2.06 tonnes of carbon dioxide. Thus, 1 tonne of wood that releases 14000 - 15000 MJ, yields carbon dioxide intensity of about 0.14 kg of CO2 / MJ of primary energy (heat, not electricity). Hard coal is about 0.095 kg of CO2 / MJ of primary energy, so wood is actually a dirtier fuel than hard coal, and therefore, it makes more sense to empty coal mines out of coal and store an equivalent amount of wood underground in conditions where it won't biodegrade, than it is to directly burn wood!
Strictly speaking, there are two heating values (higher heating value, lower heating value), so for accurate results, you can use the following chart: https://www.researchgate.net/figure/Higher-HHV-and-lower-heating-value-LHV-of-stump-wood-expressed-as-a-function-of_fig4_261922369 -- so the 14000 - 15000 MJ / tonne of dry wood (humidity 20%) figure is "LHV wet basis", meaning you burn it as-is without further drying it.