Although they are both used in carpentry Brad nails and finish nails are also both driven into the surface of wood materials using air compressor-powered nail guns. The reason that brad bails are called finishing nails is that they are usually used on products that need to have a nice “finish” in other words they may be seen on the product. Brad nails are therefore often used in carpentry for doors or molding whereas finish nails are used for detailed carpentry on cabinets and so on.
This is why brad nails have flat heads which you would be able to see, and finish nails have heads that are barely noticeable so that they will blend into the product. Brad nails are used to actually hold two pieces of wood or carpentry together and to secure the corners of furniture items. Brad nails are more robust and less likely to split and damage the article or item. They are useful because brad nails have blunt ends, finish nails would not be useful for this task because they have pointed ends which make them easier to drive into the wood or item, but it also makes them easier to split part of the materials.
Further to this brand and finish nails will differ in their size their length and their strength. For jobs such as tacking plywood together or making small items then brad nails are good for bigger items such as wardrobes or dressers or even your wooden facias on the front of your house then finish nails should be your nail of choice.
Also the type of wood you are using might affect the type of nail that you should use. Brad nails can be used for softer woods because the nails are more delicate and slimmer.
If you make a mistake when using brad nails this can be problematic as they are very difficult to remove. The nail heads will often bend or become damaged when you try to pull them out with your hammer. Then you will be left with trying to remove a nail that has no head and you will inevitably damage the wood whilst trying.
The best way to do it is to wrap an old cloth or piece of material around a spare block of wood and have that nearby. Then grab the nail with some pliers that may be as task, but you should be able to just about do it. Then you can use the claw part of your hammer and place it in between the hammer and the pliers. Use the block of wood as a brace for the handle of the hammer and slowly remove the nail this way. You may need to apply pressure to the block of wood as you ease the nail out. At worst this could leave a small hole but one that can be sanded and that will not affect the eventual finish of the item. You may have to repeat this process a few times, but it will eventually work, if you remain patient you will not cause any damage to your product.