Price is the dollars you pay.
Value is how much product and return you are getting for your money.
There is some overlap in the determination of both, however, it is certainly possible to have a $10 knife have more value than a $100 knife.
Price is determined by market factors of supply and demand. The more people that want to buy the knife for a limited number of knives available, the higher the cost to buy it. Pretty simple equation. However, we all know that the demand portion of the equation has a lot of variables and subjectivity to it. Is the knife "in fashion" or a fad? Higher price. Is the manufacturer trying to appeal only to high end buyers? This is usually seen with low quantities produced and high prices. Generally it is an artificially high price due to the "exclusivity" of the product. The fit and finish of the knife will be good, to very good. But not enough to justify the added cost. The maker has a much higher profit margin per knife, because the quantity sold is much smaller. Hard to live on selling 10 knives a year if you only clear $100 per knife. Clear $2000 per knife, at least you don't starve on those same 10 knives. But your house had already be paid for.
Value is essentially the return you get for the money you spend. But the return can be both tangible and intangible.
Tangible
If you pay $5o for a knife, and a few days later sell it for $100. That had very good value for you. a 100% ROI. Few knives have that kind of resale value, but how much you can make selling it represents one part of it's value. Other aspects that contribute to value would be:
Length of time on the warranty - plus what is covered and what isn't.
The company that made it - Warranty isn't worth spit if the company doesn't actually honor it. Or if the company is out of business, no warranty.
Collectability - Sometimes a maker who folds up or dies, adds value to the knife.
Quality of the materials used - knife that breaks or dulls when you cut your sandwich doesn't have too much value.
How much service or use do you get. A knife that will work and last for decades, has greater value than one that wears out in a couple of years.
Fit and finish of the manufacturing. Generally, it is pretty easy to produce a product equal to 90 or 95% of the similar products out there in fit and finish. Getting to that last 5-10% level can take a lot of additional time and skill. For some, "good enough" isn't. For example, say a maker produces a knife with the fit and finish at the exact same level as a Loveless or a CRK. And they sell it for $50. Tremendous value to you, but the maker is a lousy business man since he is probably working for pennies an hour.
Intangible
Personal or sentimental value to you - The knife your granddad gave to you just before he died has much higher value to you.
Personal taste - something you just love or can't get from any other product has higher value.
Uniqueness or rarity - a flint knife 100,000 years old would have little value as a usable tool these days, but have high value because there are not any Neanderthal men around to make any more.
The story - The tale behind a knife or other product is frequently used to justify the higher price/value. The art world is probably the biggest purveyor of this type of valuation. Would Van Gogh's painting be selling as high as they are if he had not cut off his ear?