Fourier Transform: interpretation of continuous spectrum at specific frequencies
You can see the non-zero magnitude of the spectrum, but the interpretation that the signal contains a sinusoidal component at a specific frequency where the magnitude is non-zero is wrong. If there is a sinusoidal component present, then there is a Dirac impulse at the respective frequency. A non-zero Fourier transform at a certain frequency is not sufficient.

The squared magnitude of the Fourier transform is the energy spectral density, and the energy inside a certain frequency band can be obtained by integrating the energy density over the respective interval.

An analogy from statistics is the difference between probability and probability density function (PDF). The values of the probability density function are not probabilities, but probabilities can be obtained from the PDF by integrating it over certain intervals.