The difference is that BHPH lots don’t want to sell to people who can pay for the cars. If they had their druthers they’d only sell to people who couldn’t even make the first payment so that they could get the car back on the lot faster, ready to take another large deposit.
When I was younger and more naiive I found a neat car at a BHPH lot. I didn’t know anything about these places - all I knew was that there was a cool Miata that I could afford to pay cash for. I went in and tried to pay cash for it, and they tried everything to get me to look at more expensive cars that I couldn’t afford. At the end of the process they told me another salesman had just sold it so I couldn’t buy it. Drove by 3 weeks later and it was still there. They’d lied so they could sell it to someone who couldn’t pay for the whole thing right away.