As I know "claim" is used in legal actions like "claim an ownership" and "demand" is used in a purchase-like act like "demand a product". Dictionary.com says a very similar description, similar at least to me. Could you please help make it clear to me?
There are two senses to the meaning of claim, and the one that matters here is
a demand or request for something considered one's due.
Notice "demand or request". You can be as meek as a mouse when claiming something, waiting in lines and filling out forms. But at the end, you expect to get the thing that's yours by right.
- If you're in an accident, and you have an insurance policy, you file a claim with the insurance company to get the money needed to settle the accident.
- if you're a gold prospector, your "claim" is the legal right to look for gold in a certain patch of land. You expect the authorities to back this up if someone else tries to dig there.
Not so "demand". A demand is up front and in your face. And it's not necessarily backed up by any right, authority, or even reason.
- A five-year-old child may demand a pony or a giant lollipop, but does that mean they're going to get one? Maybe, maybe not.
- Economists use the term "demand" as a measure of consumption, meaning how much people buy of a certain good or service. The day before I wrote this answer is known as "Black Friday" in the US, which is the day after Thanksgiving every year. There are stories associated with that day of people rushing in to stores to buy heavily-discounted items ("doorbusters"), and fights breaking out over the store's last unit of a particularly popular toy. Now that's demand.
As nouns used in legal terminology, these have similar but distinct meanings. A "claim" arises from a set of facts which provides grounds for a lawsuit. The claim forms the foundation for the demand.
An example of a claim: "John ran the red light, striking Bill's car on the driver's side. Bill was badly injured and his car wrecked. Bill is legally entitled to at least $100,000 in damages." An example of a demand: "Dear insurer of John, Your insured John rammed into our client Bill. We believe Bill is legally entitled to the sum of $100,000. Send us a check in that amount and our client will execute a release in favor of John."
In short, a demand is a form of communication, whereas a claim exists whether it is communicated or not. Lawyers ask, "Is it a good claim," meaning are there liability, significant damages, and a means to collect.