Quantity vs amount

What is the difference between quantity and amount?
They have similarity in meaning but their differences are highlighted below.
Quantity is a noun. It can be either countable or uncountable. It means the amount or number of something, especially that can be measured or is fixed. Sentences examples:
Police found a large/small quantity of drugs in his possession.
We consumed vast quantities of food and drink that night.
The (sheer) quantity (= large amount) of equipment needed for the trip is staggering.
They are now developing ways to produce the vaccine in large quantities and cheaply.
This recipe is only for four, so I usually do double the quantity if I'm cooking for my family.
It's quality not quantity that really counts.

Amount is a countable noun itself. It means a collection or mass especially of something which cannot be counted. Sentences examples:
They didn't deliver the right amount of sand.
Small amounts of land were used for keeping animals.
He paid regular amounts of money to a charity.
I didn't expect the bill to come to this amount (= of money).
The new tax caused a huge amount of public anger.
I had a certain amount of (= some) difficulty finding the house.
You wouldn't believe the amount of trouble (= what a lot of trouble) I've had with this car.