Yes and no. You're right that molecules are molecules, and where they come from might not matter very much. The trouble is that the nutritional information on the back of foods in the USA doesn't give you the full information. And really, it'd be hard to list all the information you need.
For example, protein is protein right? Well yes, but no. Probably you've heard of
complete proteins? Does the label tell you which you're getting? No. Does it matter? Maybe. Your body may be able to synthesize the ones it needs, but at what cost, and with what inputs?
You can follow this logic for all your other nutritional needs. The label gives you an idea, but it doesn't necessarily even know what to measure.