Yes Jack is right. There is a difference. If I return an unwanted item to a shop to get my money back - that is a refund. If I travel on behalf of my company and spend money on food and hotels etc. I will apply to my company for reimbursement of the money I have spent.

Yvonne's answer reflects the current usage of the two words. However, according to most dictionaries, their meaning is equivalent. Oxford: "I'll refund you for the apples and for any damage" "The investors should be reimbursed for their losses"

Does this system work?

No difference. The second one has french origin from "remboursement", which means ''refund'' in english.

If you return an item that you bought to a merchant to Exchange it for the money you purchased it with then you are getting a refund. If you are being given money for expenses that you have on behalf of someone then you are getting a reimbursement.