Do the words 疼痛 and 痛苦 exactly mean "physical pain" and "mental pain"(i.e. sadness), respectively?
疼痛 means physical pain, but it is very formal, and usually used in medical speak. This is also similar to 痛楚, which is also too formal for casual conversation.
For example: 肌肉疼痛是感冒病徵。 ~Muscle pain/aches is a flu symptom.
The words 疼 and 痛 are usually used in solidarity, in Mandarin and Cantonese respectively.
For example: (In Mandarin) 我肚子疼。(In Cantonese) 我肚痛。 ~I have a stomachache.
On the contrary, 痛苦 means pain in general. It could still be physical, but usually mental or even metaphorical.
For example: 生產的過程很痛苦。 ~Giving birth is painful.
Bad example: 他看來很痛苦。is as vague as &quot;It looks like he is in pain&quot;. It could be physical or mental, and depends on the context.
Another example: 學習中文很痛苦。 ~Learning Chinese is painful. (Based on true experience)