Comparing these two definitions from OxfordDictionaries shows the two words obviously overlap...
embarrass - cause (someone) to feel awkward, self-conscious, or ashamed
ashamed - embarrassed or guilty because of one’s actions, characteristics, or associations
But two key differences are...
1: embarrassed more often applies to socially awkward contexts, rather than regret, guilt
2: You don't usually feel embarrassed when you're alone
I don't really like OP's idea that being ashamed is more "serious" than being embarrassed. I might feel ashamed if I discovered I was the only person in my road who didn't leave a Christmas tip for the postie, but that would be nothing compared to how embarrassed I'd feel if I discovered said postie knew exactly what was in all the packages she'd delivered over the preceding year!
TL;DR: Shame is mainly a response to having transgressed your own (internal) moral code. Embarrassment is more about feeling that others may laugh or look down on you for something you did.
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
Shamed is what one does to you.
Ashamed is about how you feel about yourself.
Shamed could be punitive, ashamed shows remorse sometimes repentance.
If a person has no shame, then others might view their behavior or conduct as shameful and thus shame them, but the individual who has no shame is not (yet) ashamed of anything they have done or are doing.
Below is paraphrased from Webster's fourth edition
To shame is to dishonor, or disrespect
Shamed is when others treat with dishonor and disrespect due to some action or trait of the one being shamed.
Ashamed is when you are embarrassed by these same traits - or when you fear shame/dishonor/loss of respect even before said actions are publicly known