I've linked below to a great website explaining the difference between a traditional statement and a contribution margin statement.
Variable costing is also known as direct costing or marginal costing, and it excludes the fixed manufacturing overhead in its calculation of per unit product cost. Variable costing is the method that features a contribution margin on a revenue statement.
The equation for net operating income under variable costing is:
net sales revenue - variable costs - fixed costs = operating income.
The difference between the net sales revenue and the variable costs is often called the "contribution margin."
Its alternative, absorption costing (also known as full costing or traditional costing) is different specifically in how the per unit cost in calculated. The difference between variable costing and absorption costing is that the fixed manufacturing overhead is included as a product cost under absorption costing. So, in order to employ absorption costing, we have to compute a per unit production cost, including the fixed manufacturing cost.
The equation for net operating income under absorption costing is:
net sales revenue - costs of good sold - selling and administrative costs = operating income.
Because absorption (or traditional costing) considers only the goods sold, the net revenue yielded is often higher. The focus here is on the income generated, without specific consideration of the relative weight of the variable or fixed costs (which are, as the name suggests, "absorbed" into the unit price). This is the format used primarily by external parties, as it is the accounting standard practice.
Variable costing, on the other hand, is often used internally in order to showcase more precise comparisons in revenue. It is useful especially when comparing, for example, the profitability of two types of products.