I understand your doubt,
You need to blame the English Language for that confusion. There are two words related to hunger. HungER and HungRY.

HungER is a sensation, and it refers to one or more of the bodily sensations together which send a message to the brain that you should eat. Eg. as mentioned, light headedness, rumbling tummy etc

When the message is sent, your mind in turn tells you to eat, by making you feel HungRY. so this is a feeling arising in your mind.

Similarly, say after too much physical exertion, you may in turn get leg cramps, drooping eyelids etc, (which are physical sensations), many such sensations reach the brain. so from body to brain. There is no single word for these arising in the body collectively. (unlike the case of hunger)
But after the brain interprets it collectively, it itself gives you a message of being Tired, so it arises in your brain, thus a feeling. (which would be now similar to how we figured hungry as a feeling)

As badly as i want to, i am not very good at explaining stuff.

Apologize if it is getting repetitive. Don't know any other way of explaining lol.

Anyway, as long as you understand what message the body sending, does the classification matter?