In simple and layman terms, they are the same in meaning in some usage during conversation. But in professional reports, writeups and discussion, their usage in sentences should be distinguished.
In finance and business, cost is usually used to connote historical cost or the money used to acquire something (eg original amount paid for goods, services and assets). An example of its use " It cost us USD700 to get his services" or " The goods we are selling right now has a cost of USD100 but we we sell it USD350".
Value as used in business connotes the amount of money that say, an asset has for a certain time period whether at present or any other time. It is necessarily the amount of money paid for to acquire something since it can be an amount arrived at which is the result of estimates and assumptions. Value can also be the sum of original cost +/- estimates and assumptions. Hence, the term " Present Market Value" is an amount arrived at using present market factors such as demand, the avilability and going rate of the same item in the market etc.. Another example is 'Net Book Value" or " Depreciated Book Vlaue" which is usually the difference between the Original Cost less the calculated depreciation. We do not use "Net Market Cost" or "Net Book Cost" since it will confuse people.
Price, like Cost, is usually used to denote the amount needed to pay something for purchase. The main difference in its use as against the use of Cost is the point of view of the writer or the speaker. It is better to ask a vendor " What is the price of your goods" instead of "What is the cost of your goods" since the vendor may give out his original cost (without markup) and the conversation is now misleading.
For a businessman, His price is his original cost + his profit markup while his cost is the original cost he paid to acquire ownership of the goods and resell it at his own price for a profit.
In discussions when someone asks " What price did you pay to get this goods?" , the answer can be limited to only the purchase price NOT including the freight and handling and other cost which form part of the total cost of the goods. If the question was " How was the cost of the goods?" The answer should be the overall sum of the monies paid for the goods (purchase cost +freight and handling etc..) Hope I made sense.