Access is the whole difference
Dealer-only auctions require a dealer licence, and they move enormous volumes of trade-ins, fleet returns and lease turn-ins. Public auctions are open to anybody, and they consign a mix of private sellers, estates, repossessions and whatever the dealer channel did not absorb.
The pricing is not as different as people assume
Buyers imagine dealer auctions as a wholesale paradise. In practice, professionals bid against professionals there, and the market is efficient to within a few hundred dollars. The real difference is that dealers buy at volume and accept risk they can absorb across fifty cars a month.
Disclosure is usually better in public
Because a public auction sells to people who are not in the trade, the good ones compensate with inspection reports, photographs and written condition disclosures. A dealer lane often runs on a light announcement and the assumption that the buyer can assess a car in ninety seconds.
Which should you use
If you are not a dealer, this is not a choice you have. The useful version of the question is what to demand from a public auction: a written inspection, photographs you asked for, a VIN you verified yourself, and terms that say what happens if the vehicle is not as described.
From the auction floor
See how this works on a real lot.
Every listing carries its inspection report, its full specification and its bid history. Read one before you decide what it is worth to you.