There are two BoP settings in the game: BoP On/Settings Disabled and BoP On/Settings Partially Allowed.
With Settings Disabled, ungrouped cars will be reverted to stock power and mass, and all aftermarket parts equipped on the car (except tyres) will be temporarily reverted to stock, even "permanent" ones like Stroke Up and Increase Body Rigidity. Any GT Auto parts like wings, wheels, and roll cages will still be physically on the car, but their performance effects are negated while under BoP. Wide Bodied and Engine Swapped cars are ineligible to enter BoP events. Any grouped racecar will have their power and mass adjusted to its group (so a Skyline Super Silhouette will see massive buffs while a TS020 will be massively nerfed, even if they both ran in the same race with each other.)
With Settings Partially Allowed, in addition to adjusting power and mass to stock for ungrouped cars and changing power and mass per BoP for grouped racecars, the game will create a temporary setting sheet for the car as long as it's in the event, using all the parts the car originally came with and starting at their default values. This means that a car has to come originally with adjustable parts to change the parts' settings under BoP/Settings Partially Allowed, and that players have to manually adjust the settings to their liking each time they enter an event, with no way to save and load their settings under BoP. (this is a QoL thing players have been complaining about for a while now).
Take for example the Amemiya RX-7. It comes default with an adjustable rear wing, but no Brake Balance Controller. I can buy a Brake Balance Controller for the Amemiya RX-7 in the tuning shop and equip it, but in a BoP/Settings Partially Allowed lobby, I'll be able to adjust its rear downforce, but not its Brake Balance.
It's a little convoluted, but I hope this helps clear things up.