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.

Yes, this is why pepper spray sucks even if it doesn’t get in your mouth.

Spicy isn’t a taste or a smell, it is a sensation caused by the compounds lowering the threshold to activate of heat detecting nerves too below the ambient temperature of the human body. It’s basically making you burn your self.

Lots of other “flavors” are also like this, lowering the threshold of firing for certain sensory nerves. Sichuan pepper for instance, it lowers the threshold for movement sensing, causing the bizarre tingle waving sensation.

Those heat sensing compounds exist all over your body, not just in your mouth.