A concession means the private company operates the railway for a set fee and a set operational standard, the state owner will retain ticket revenue (and risk). This is how the London Overground concession works.
A franchise basically gives all operation responsibilities and ticket revenue to the private operator, in return, the private operator gives a lump sum bid for the contract at the beginning.
A franchise basically gives all operation responsibilities and ticket revenue to the private operator, in return, the private operator gives a lump sum bid for the contract at the beginning.