Harmonics are integer related to the fundamental, whereas partials need not be.

Evidence

The individual sine wave components of the waveform are often called the partials of the waveform. If they are integer related, as in the square wave, then they can be called harmonics. The lowest frequency is called the fundamental, or first harmonic, and the higher frequency harmonics are labeled according to their frequency multiple relative to the fundamental. Thus the second harmonic is twice the frequency of the fundamental and so on. Partials on the other hand need not be harmonically related to the fundamental, and are numbered in their order of appearance with frequency. — David Howard, Jamie Angus, coustics and Psychoacoustics, 447

Categorization

• DEFINE: Distinguishes harmonics (integer multiples of the fundamental) from the broader category of partials (any sine component, numbered by frequency order).
• XREF: connects to: Spectrum components are partials and only integer-related ones are harmonics — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 450