What is the difference between Cost of Manufacturing and Cost of Goods Sold

The costs of manufacturing are made up of direct materials, direct labor and overhead. How you calculate it depends on a lot of things. For one, it depends on whether it's total manufacturing costs for a month, the total that's in the WIP account at a given point in time, etc. When it's homework, calculating anything always depends on what info is given in a problem.

Cost of goods sold is the same exact costs. The only difference is that it's the costs that have gone into whatever has already been sold during a period. I.e. You have costs to manufacture it, and then when you sell it, it's the same costs, but it's now the costs of what you just sold. There's different ways it can be calculated, and again, if it's for homework it'll depend on what information you've been given.

Cost of manufacturing has two parts:
1, Total Manufacturing Costs - these costs comprise the costs incurred during a period, such as raw materials consumed, direct labor and manufacturing overheads incurred.
2. Cost of Goods manufactured - this figure is arrived at after adjusting the work in process inventories from the total manufacturing costs.

Cost of goods sold is the total manufacturing costs adjusted for the finished goods inventories.

As regards their importance in accounting standards, I am sure you must have read the framework on preparation and presentation of financial statements which forms the basis for the issuance of the individual accounting standards.

The Framework states that the financial statements should be useful for making decisions. IAS 2 relates to Inventories. Now how can you put value on finished goods or work in process until you have the total manufacturing costs and the cost of goods manufactured.

To understand how exactly these figures are worked out, you must study your text book, concentrate on the examples and try and soleve some of the exercises and problems.