If your arm is tender, then bumping it causes pain. If your arm is hurting, then you feel sharp pain continuously. If your arm is sore, then you feel a gentler pain. Soreness is often used to describe pain from overexertion, or pain that is only felt upon movement.

Sore - Painful to touch, Tender I have a sore spot on my head and cringe every time I comb there. Tender - Easily hurt, Sensitive Because I've been on the computer so long, my head has become tender. Hurting - To be in pain After the concert, my ears were hurting really bad.

agreed with richard