Two entirely different questions:
To buy at an AUCTION; the Trustee Sale, you will need to bring all CASH; are you prepared to do that?
The houses at the Trustee Sales usually go back to the Bank, as they offer the amount of the LOAN, which is more than you would offer.
To buy at a private AUCTION; you would need to be very, very careful; usually you do not know what you are buying, do not have the opportunity to inspect, do not know about any LIENS, and basically have no protections.
To buy a FORECLOSED house, you would need to have a Buyer's Agent, to help and protect you: The Banks are so careful about this, that they are paying that Agent's commission for you.
Good luck and may God bless