Economists tend to be sloppy with their terminology.
"In economics, demand is the desire to own anything, the ability to pay for it, and the willingness to pay. The term demand signifies the ability or the willingness to buy a particular commodity at a given point of time."
Note the "ability to pay for it."
I go with a more strict definitions, the actual occurrence of the purchase of the product, the quantity demanded and the price it was demanded at. It is the measurable and observable activity that take place. This is a fundamental aspect of the science, any science.
We can infer that there is excess demand or what I like to call potential demand.
The demand curve is what the demand would be if the price was this or that. It is, unfortunately, not observable. The if is a big part.
We cannot observe or measure a persons willingness, desire, or need except in that they act.
The sloppiness leads to all manner of misinterpretations based on the assumption of something existing that, in fact, is not measurable.
If someone orders a thing, we can measure that as potential demand. If they put a deposit down on it, then the probability of that being demand increases significantly as we can measure the percentage of people that will give up their deposit. If they pay full price before receipt, well, they get the product they paid for whether they want it or not later. Unless, of course, they get a refund in which case there was no demand in the first place.
Maybe, there in lies part of the problem the lack of differentiating potential demand, if they had money and could make the purchase, from actual demand and quantity demanded. Why should we need to increase demand during the recession, there is plenty demand, what we need is to increase production. Production requires labor which then has money so they can actually express that demand.
There is a difference between some latent internal feeling and an observable behavioral feeling. Someone eating is hungry, we can observe that. "I feel hungry" is not an observable behavior. Many people feel hungry, but do nothing about it because, "I'm not THAT hungry, I'm to busy to eat." Well, then they really aren't hungry then are they. If they were really hungry, they would stop and eat.
Science cannot measure "desire". And when we start using subjective qualities to discuss it, it becomes confused by every manner of subjective interpretation.
We can hardly and definitively say that someone was "willingness to buy a particular commodity" if they said, "Yeah, I want it" then when they didn't actually buy it when it became available. For all we know, they don't know what they want. If they were actually willing, they would have actually done it.
We can check a persons ability to buy, based on income and expenses. We can infer the possible demand based on the change in the rate of sales. But we cannot measure desire or willingness to pay until they actually do it.
I have to say, economists are sloppy in their terminology. It is a hard science when we make it a hard science. And I suspect that, if we go back in the record of history of economics, we would likely find that the original usage was as observed.
If you stick with the "as observed" you cannot go wrong. if you cannot base the understanding on observation, you cannot have knowledge.