Cost is what is exchanged for something else. This is not always apparent. For instance there is the idea of opportunity cost, which is that the cost of an action is the sum of alternative actions.
Cost also includes the long term affects. For instance, if you buy a car, the price may be $20,000. However the cost of owning a car includes gas, maintenance, insurance, etc. This is usually called the total cost of ownership.
Most people look at the price tag, and ignore the cost completely. Common decision discussions include things like "Can I afford the payments?" or "Do I have enough money to get X?" Those are the wrong questions to ask yourself. We should be asking ourselves if acquiring something fits in with our long term goals.
One example of cost versus price thinking is college. It is so ingrained in our society that when people leave high school they should go to a four year university. However, there is the opportunity cost (lost wages and experience while going to college) and total cost of ownership of a college degree (including interest payments). Ten years ago it was probably worth it to go to college directly out of high school. However, college tuition inflation skyrocketing since 2001, the value of a four (in my case four and a half) year degree has to be evaluated.
Of course our society, when dealing with inflation, turns to debt. College tuition no longer affordable? Finance it. Student loans don't require payments until you graduation (reminds me of the furniture store ads for no interest and no payments for the next N years). But do you receive enough value from a college education? Is there a way of receiving the same benefit for less? I don't know the answer, but it is something that we need to start looking at.
Another example is home ownership. Most people rely on the lender to determine how much home they can afford. I've heard that a good rule of thumb is that your payments (Principal, Interest, Taxes and Insurance) should be no more than 25% of your gross income. I've heard that lenders will offer you up to 40% of your gross income. Personally, I'd feel better if it was closer to 0%. Again, as home values rise and people feel they require a certain type of home in a certain area, they turn to debt to solve their problems. However, the cost of a home is much more than the Principal, Interest, Taxes and Insurance. There is maintenance, upkeep, repairs, window coverings, etc. The cost of owning a home is much higher than most people realize.
With both student loans and mortgage, when we turn to debt (because we cannot afford it) we are actually paying much more than the original price. The actual cost of a college degree or home ownership becomes astronomical as we turn to debt to solve our inability to pay the price.