Not always. Black pepper contains Piperine which also effects the TRPV1 sensing protein like capsaicin, if a bit weaker. Horseradish, mustard and wasabi have Allyl isothiocyanate which affects TRPV1 but also TRPA1 which triggers pain cold and itching response, leading to coughing and tearing.

There are a fair amount of other compounds that effect the TRPV1 and plenty of other similar receptors.