demand: a list of prices
and the quantities that would be purchased at those prices,

holding all other things constant.

The demand is the entire curve.

quantity demanded: the quantity bought at a particular price.

It is a point on the demand curve.

Equation of demand: q=f(p)

Inverse demand: p=f(q)

Law of demand: a higher price never results in
a greater quantity demanded as a substitute good.

The law of demand depends on the substitution effect:

when a price changes,

buyers substitute lower-priced goods for higher-priced goods.

A change in price also has an income effect.
It changes the quantity demanded, but this is not part of the law of demand.

supply: a list of prices
and the quantities that would be sold or rented at those prices,

holding all other things constant.

quantity supplied: at some price.