As verbs, the two can mean the same, as weevil points out: to pay specific attention to an object or action that one performs.
When that meaning is what you want to convey, the two are indeed interchangeable.
However, both verbs have other meanings as well, and they do certainly not mean the same.
I can, for instance, focus a camera (or more precisely, a lens) or I can focus a light beam (by use of a lens).
I can concentrate a solution (making it "stronger"), items can concentrate around a central point.
The short answer: when used as a noun, the "price" is the amount charged for something, and the "cost" is the amount paid for something.
When a person is discussing buying something at retail, the most common noun used for the amount charged by the seller is "price."
I wanted to buy a white cotton jumpsuit, but the price was too high, so I didn't.
When used as a noun, "cost" refers specifically to the amount paid by someone for something. It is most often used in an accounting or business context.
Our cost per item is three dollars and our gross revenue per item is sixty dollars. That's a fifty-seven dollar profit on each jumpsuit sold!
It is not exactly wrong to use "cost" as a noun in the same way you would "price":
I wanted to buy a white cotton jumpsuit, but the cost was too high.
However, this is not as idiomatic, at least in American English; it sounds a bit melodramatic. You would be more likely to use "cost" as a noun where it is understood that you are discussing the impact on your finances, rather than the amount the store asked for the item:
Sure, it was expensive, but the cost isn't what's important: it's how the jumpsuit makes you feel.
Confusingly, you can use "cost" as a verb to describe the amount charged for an item:
That's a lovely jumpsuit; how much does it cost?
"Price" as a verb is used only for the act of setting a price:
Why would you price these jumpsuits so high? We poor students need jumpsuits, too!
Best Answer
Both words can be used to describe when a person is frightened (although, typically, I initially think of shivering in the cold, and shuddering at a thought).
I also think of shivers lasting a little longer than shudders. I might say, "I was shivering at the bus stop for almost twenty minutes!" but, "When I stepped outside, I shuddered in the cold," referring to a momentary shudder.
Likewise, if a young child trembled in fright during a scary movie, I might say he "shivered through the movie," or "shuddered at a scene." However, I must point out there are no hard rules about this; these are just ways I typically use these two words.
Shiver is also used in the expression "Shiver my timbers!" – which I don't hear very often, unless someone is trying to do a humorous imitation of a pirate.