Short answer: Auction = highest bid wins, no conditions. Negotiation = back and forth offers. Tender = sealed bids by deadline.
Auction: highest bidder wins on the day. No conditions. Risky for first home buyers. Negotiation: you make an offer, they counter, you agree. Most common. Tender: all offers submitted by a deadline, seller picks the best. Tender can include conditions unlike auction.
Auction: Bid to $620,000, win, must buy unconditionally
Negotiation: Offer $590,000, counter $605,000, agree $600,000
Tender: Submit $595,000 with finance condition, wait for decision