By whatever name, trenching, cuts, channel or profile, these methods all aim to take hard rock samples (as opposed to stream and soils which are loose transported material) for gold analysis.
Trenching is done on scales of several meters up to several hundreds of meters and maybe done by hand digging or using an excavator. Trenching would be the logical next step if a gold anomaly is found in soil sampling. It helps to get an accurate view of the extent and content of gold in the rock. If trenching results are positive, drilling would follow.
Because trenching aims at taking samples of rock rather than transported material, the confidence of the results increases because there will be no dilution of grade in the samples as occurs in soil sampling. Because of the accuracy of trench sampling, the results can be used later in resource calculations (assuming this was done at a later stage after drilling is also completed).
Because trench sampling is a more manual process than drilling, there exists the risk of sampling error due to samplers selectively sampling those parts of the rock that carry gold grade. For example gold may occur within quartz veins which make up 20% of an area of rock but the sampler collects a mass that is 50% quartz veins, and so the results are then 2.5 times the actual gold grade. In some cases angle-grinders are used to ensure even sampling and limit such sampling errors.