Differences between the Basic and General methods
The two method approach the question differently. The general method tries to incorporate mesomeric, tautomeric rearrangement, as in 2-pyridone, while the basic method does not. In the basic method the external double bond breaks the formation of aromatic ring.
The 2-pirydone is aromatic due to its mesomeric rearrangement:
    
        
The following molecules will give different results depending upon the method applied.
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         Molecule in aliphatic form  | 
                
         Basic aromatization  | 
                
         General aromatization  | 
        
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         IUPAC name: pyridin-2(1H)-one  | 
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         IUPAC name: 2-thioxo-2,3-dihydropyrimidin-4(1H)-one  | 
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         IUPAC name: 2,4-dihydro-3H-1,2,4-triazol-3-thione  | 
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         IUPAC name: 9H-xanthen-9-one  | 
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         IUPAC name: 5-thioxo-1,2,4-triazolidin-3-one  | 
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         IUPAC name: imidazo[1,5-a]pyridine-3(2H)-thione  | 
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