This is a great post on the difference between the two (with respect to energy) by Bob Murphy.
I personally think a lot of Julian Simon boosters are terrible about how they make this point (I have one in mind in particular... see if you can guess who), and they beat well-meaning people over the head for thinking something very reasonable: that there is a physical finitude to certain resources.
I like Bob's take on it here because it takes care to point out that that's not really wrong at all, it's just not the most useful way of thinking about the issue.
I also think that saying "we should really be talking about about economic scarcity rather than physical scarcity" is better than beating people over the head for mentioning scarcity in a more colloquial sense because the economic argument isn't necessarily the cornucopia that some people present it as either. Innovation and the adoption of alternatives is driven by rising costs, which can be... well... costly. So reorienting people towards thinking about the right thing can get them to focus on those very real issues.
I haven't read the CAP report he's criticizing, so I'm not sure if I'd endorse his criticism in toto (I know you're all shocked I'm not taking Bob's read on them at face value). To the extent that the report is driven by the sentiment that these are scarce physical resources and therefore we need to diversify immediately, I'm obviously more on Bob's side. To the extent they are making an externality argument I think it's more tenable. To a free market economist like myself, there's an inherent artificial reduction in the cost of fossil fuels relative to their true cost. And as we know, that sort of market distortion can retard innovation and adaptation.