The brand follows the vehicle permanently
When an insurer totals a car, the title is branded salvage. Repaired and re-inspected it becomes a rebuilt title, and that stays with the vehicle through every future sale. It is public information and it is the first thing a carrier sees.
Liability is easy, physical damage is not
Most carriers will write liability on a rebuilt-title vehicle. Comprehensive and collision are a different matter: some decline outright, some write it at a reduced value, and the valuation after a future loss reflects the brand. That is worth knowing before buying rather than after.
The discount at purchase reflects a real cost
A rebuilt-title car is cheaper for reasons that persist: harder to insure fully, harder to sell, and uncertain repair quality depending on who did the work. It can still be a sensible purchase with open eyes, which is a different thing from a bargain.