To soar is to fly high or rise sharply — prices soared, an eagle soaring. Sore means painful, and as a noun a painful spot. Rising takes the A; pain takes the E.
The core difference
Rising and hurting.
- soar — rise or fly high: soaring costs, soaring architecture.
- sore — painful: a sore throat, a sore point. Also informally: aggrieved.
The figurative uses
Soar is very common in reporting for sharp rises — soaring inflation, soaring demand. A sore point means a subject that causes irritation, and a sore loser is one who takes defeat badly. Both figurative senses are standard.
The related word
Sorely means severely or greatly — sorely missed, sorely tempted. It comes from the pain sense but no longer implies pain, which surprises people.