Is it necessary to quantify each standard with its specific compound, or can I use a single standard to quantify two different compounds with the same chemical structure, for example?
The chemical structure and physical and chemical properties of the standard substance should be as similar as possible to the substance to be measured, but it is not necessarily required to be 100% consistent in structure, so I think the situation you said is OK
If the extinction coefficient is the same at the same wavelength, you might be able to use the same standard for two different compounds. Otherwise, you need separate calibration curves. If the compounds have different extinction coefficients, they will have different concentration/absorbance response curves (which should be linear). If different wavelengths are used, the lamp and detector combination will cause different response to a compound, and the extinction coefficient will likely be different. On for the mass spectrometer, different compounds may well ionize or fragment differently, causing differing response from the MS. To be sure that the two compounds behave sufficiently similar to one another, one needs to run the experiment to prove the correspondance.