Volunteers and compensation
If your flight is overbooked, the Denied Boarding Regulation says the airline must ask for people to volunteer not to fly 'in exchange for benefits'.
If there aren't enough volunteers, the airline can free up seats by denying passengers the right to board the plane.
If you volunteer to give up your seat, you're entitled to a refund or rerouting and also 'benefits', which you have to negotiate with the airline. Note that there are no parameters as to what benefits the airline should offer.
If you don't volunteer, or can't agree 'benefits' with the airline, and you're denied boarding, you have the same entitlement to assistance and compensation as you'd have if your flight was cancelled. The only difference is that you're entitled to the compensation straight away.