That's correct.
GDP is used to measure the value of economic activities in each country in its own currency, and when cross-country comparison is made then data are converted into a base currency (e.g. US$) at current market price. It is useful tool in gauging relative size of economies, trade situation, investment, debt, etc. Since its induction back in 1934, the concept has evolved and various approaches have been practiced, the latest universally agreed principles would be the SNA 2008.
When measuring purchasing power of individuals (per capita) especially in special demographic segments like the lower income groups or poverty (e.g. World Bank use $1.25-2/day per capita PPP-adjusted as poverty line), who have less chance of accessing the international market, their purchasing power will need to be adjusted to what they can actually purchase. The method of adjustment is hardly universal, considering that people are purchasing different commodities (e.g. food, clothing, housing) even in the lower income groups, and that in the intertwined supply chain people could be purchasing indirectly from the international market (e.g. energy).