It depends on where a person wants to put “emphasis”.
C3H7COOH draws a person’s attention to the COOH [functional group](https://en.wikipedia.org/wiki/Functional_group) that gives the chemical its carboxylic acid properties.
CH3CH2CH2CO2H is like a text version of the chemical structure.
C4H8O2 counts the atoms in the molecule but obscures the structure, which means it could also refer to the chemical isomer, isobutyric acid.
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