That can get very convoluted depending on the issue; for instance, i bought my model s 90d used from tesla because they advertise it passing a 70-point inspection and I assumed they'd be better the safest bet to purchase from with their warranties. Quickly needed to replace a rear tire because the alignment/balancing was off---but shops won't do that for teslas so I had to replace a tire and then pay $500 to tesla service to try to prevent that from happening again....they claimed it was due to having staggered tires as well as just normal wear and tear, but neither were true. Not long after, the same tire wore down to the cords on the inside....thankfully my longtime tire shop replaced it but tesla service was wholly unresponsive when the only logical cause was not properly aligning/adjusting the camber. Further...my own adjuster checked it out, noticed an aftermarket weld on the rim that was 100% from pre-purchase as well as battery damage from the time it was towed to a tesla shop and he could check it again....none of which tesla said was covered.
In short--teslas used warranties are garbage and their customer service is worse than garbage. Depending on the third party, you might have better chances. Tesla has been on a steady decline and their best warranty perk is for the battery...but most people don't seem to have issues with that. Things like the door handles misfunctioning, screen glitches, etc...can often be fixed on your own