Maximum bid and proxy bid are the same things. To place a proxy bid, just enter the maximum amount you are willing to pay. After submitting your maximum bid the proxy software will raise your bids with the minimum increase necessary to win the bidding (up to your maximum bid).
Using proxy bidding you can win the item at the lowest possible price and you do not have to follow the bidding manually.
Your maximum bid is only placed when a competing bidder bids the same amount.
Once another bidder places the same bid you will remain the bid holder as your bid was received first. Your maximum bid will never be displayed to other parties.
Please note that if the current high bidder's maximum bid is higher than the bid you place, you are immediately outbid because your bid is not high enough to beat the earlier maximum bid.
Note: Your auto bid amount can jump above the next bid increment if another bidder has placed a higher auto bid.
Also, your bid will be entered at the lowest price for which the consignor is willing to sell the item. (the reserve price)
If you have already placed a bid, and you place afterwards a higher (proxy) bid; your initial bid will not be raised.