I had a two-page paper on the difference between unselfishness and selflessness but I decided to spare you my rantings.Here is my thought in a nutshell, though:
The difference between unselfish and selfless is the difference between cost and gain. They are opposites. A person acts unselfishly when he/she does something for someone that will benefit the other while the gain is negligible.
On the other hand, a person acts selflessly when he/she does something for someone that will benefit the other while "doer" experiences a cost factor.
The more selfless the act, the higher the cost.
The more unselfish the act, the lower the gain.
The ultimate act of selflessness?
Doing something for someone that will give great benefit while costing you everything.
The ultimate level is when the deed is done for those who hate you.
Romans 5:8
But God demonstrates his own love for us in this: While we were still sinners, Christ died for us.
