People sometimes talk about upward-sloping demand curves occurring as a result of conspicuous consumption- specifically, the high prices increases the status of a good and makes people demand more of it. While these sorts of goods do in fact exist, they are different from Giffen goods because the increase in quantity demanded is more a reflection of a change in tastes
for the good (which would shift the entire demand curve) rather than as a direct result of the price increase. Such goods are referred to as Veblen goods
, named after the economist Thorstein Veblen.
It's helpful to keep in mind that Giffen goods (highly inferior goods) and Veblen goods (high-status goods) are at opposite ends of the spectrum in a way, and only Giffen goods have a ceteris paribus (all else held constant) positive relationship between price and quantity demanded.