Your Analogy is bad… and you should feel bad!
A bad analogy can frame an entire conversation improperly. This is one of those “anecdotes from a middle-aged man posts.” So take it with a grain of salt.
A number of years ago I worked in the risk management team for an insurance company that sold long term care (LTC) insurance. LTC insurance is a private product that covers home health care and nursing home care if the policyholder is unable to take care of themselves on their own. I got to be friends with the new product design team as well as some folks in sales. So I asked them to explain how they sold our LTC insurance products.
Interestingly enough, the sales guys would frame the sales pitch as choosing between a Chevrolet and a Cadillac. The Chevy product was the base insurance policy without a lot of features. Just a simple product that pays up to $X dollars per day after you exhaust a deductible of $Y dollars. And it has a maximum payout of $Z. The Caddie product, on the other hand had all sorts of features like a much lower deductible, many more complicated policy choices and, most importantly, always cost more than the Chevy. If I recall, the main reason the Caddie product cost more was because the deductible options were pretty low.
If I had two put options which were exactly the same except one had a strike very close to the current market price and the other had a strike two standard deviations below the market price, it would be insane to call one a Chevy and the other a Caddie. They are just priced differently because they have a different probability of ending in the money.