I would argue that the 'resource curse' is more often conflated with a similar, but related (indeed, deeply intertwined) problem where single-export economies (economies that depend on a relatively small number of exports to generate revenue) tend to rely on volatile commodities (oil) that can dramatically impact the economic health of a country when the price of the good varies significantly over time.

The 'resource curse' speaks more to the fact that extremely profitable natural resources typically, but not always, tend to leave wealth sequestered in the hands of corrupt political elites, that economies based on export trades of natural resources are highly vulnerable to price fluctuations and declining finite reserves, and that (perhaps most importantly), economies that focus on single commodity exports tend to exclude development in other industries. The entire country becomes dependent on a single export (agricultural products in Central America, oil in Venezuela, colonial economies in Malaysia, Indonesia, Africa, and South America), which in turn results in domestic economics geared entirely for a specific good. That's not a healthy economic model.

The petroleum industry in Alaska, North Dakota, and Canada is greatly beneficial to the local economies, so long as those fields remain economically productive to maintain. Moreover, those are localized subsets of a broader, more diversified national economy. The entire country's economy, laws, and political system isn't geared towards a single export.

Lastly, single-export economies are typically more vulnerable to exploitation and abuse by the existing (usually authoritarian, speaking from the 1970s onwards) government. The basic idea is that authoritarian governments with a valuable export (oil, for example) are not under pressure to spend tax dollars in a just and fair manner; rather, authoritarian governments 'buy off' their populations with social programs and other benefits. That is, of course, an untenable proposition in the long run, which tends to lead to civil discontent, public outcry, and domestic unrest. This vulnerability to abuse is compounded by the fact that, from the 1970s onwards, untapped natural resources located in authoritarian regimes are more likely to be exploited by agreements between the ruling elites and cash-rich foreign multinational corporations (the elites allow the companies in, provide security while the corporations in turn generate shockingly high profits for the local rulers). None of that is a recipe for an honest democracy.

TL;DR of it all is something akin to the following:

Single-export economies are highly vulnerable to price shifts, political unrest, and abuse from their own corrupt ruling class. While an abudance of natural resources is not inherently a bad thing, it does tend to lead to less-than-ideal outcomes in nations where existing authoritarian or corrupt governments exist. Moreover, single-export economies tend to disregard economic diversification. Economies that send only raw materials out and receive finished goods in return and never attempt to change that relationship are not particularly sustainable.