I saw people use soil organic carbon and soil organic matter interchangeably. How are these terms related and is more appropriate to use in scientific arena?
Soil organic carbon (SOC) is an important and widely used soil biological parameter. Organic matter is ordinarily and incorrectly used to portray the same soil fraction as total organic carbon. But the fact is that soil organic matter is different from total organic carbon, because soil organic matter includes all the elements H, N, O, etc. which are also part of organic compounds, not only carbon.
Soil organic carbon (%C) = Soil organic matter x 0.58
However, while this simple mathematical transformation seems to suggest an equivalency between the two, this is not true, because SOM can come in many different forms with a wide range of attributes. While two types of SOM may have the same SOC content, their behavior and importance for soil fertility may be very different, depending on whether they are dominated by very complex and stable compounds or by easily degraded materials. In addition, different types of SOM will liberate different amounts of nutrients, will have different capacities to retain water and nutrients, and their composition will make a big difference to soil organisms, depending on their digestibility and other attributes. So, just reporting SOC can hide many essential aspects which could be described by characterizing SOM according to its composition and attributes.
Soil organic carbon (SOC) and organic matter (OM) both are related to each other. Total organic carbon is different from SOM. If we know the SOC we can calculate the SOM and vice-versa by multiplying the standard factors.
Soil organic carbon (SOC) refers to the percentage carbon component of organic compounds. SOM is composed mainly of carbon, hydrogen and oxygen, and has small amounts of other elements, such as nitrogen, phosphorous, sulfur, potassium, calcium and magnesium contained in organic residues. SOM can be calculated by multiplying SOC with 1.724 factor.
While not answering your question directly, I would like to draw your attention to some insightful material about soil carbon (and the difference between stocks and flows of carbon) by former pastoralist Alan Lauder on the website of The Royal Society Of Queensland. It could be useful background for your project.