If you submit your property for Auction this means that prospective purchasers will bid against one another at a date and time suitable to you.
You can set a reserve price, which is the minimum you will accept, and once bidding has passed that level you know you have a sale, as it will be unconditional and a predetermined deposit must be paid on the day.
Sale by Private Treaty means that you set a price at which your property is to be marketed to the public through the marketing plan agreed to by you and the agent.