Topical minoxidil is an FDA-approved hair loss medication that does not require a prescription whereas oral minoxidil is considered an off-label prescription for hair loss and does require a prescription. "Off-label" means it's not FDA-approved for that particular use, but can still be prescribed at the provider's discretion.
Topical and oral minoxidil contain the same active ingredient. While there have not been clinical studies comparing their efficacy, there appear to be some benefits of using an oral treatment method vs. a topical medication method, such as more precise dosing and better medication adherence & consistency.
Some people may also benefit less from topical minoxidil due to lower levels of a specific enzyme in their hair follicles (follicular sulfotransferase). Oral minoxidil may be an effective alternative in this case, as the medication is absorbed systemically and is thought to be activated by the liver.
Some people may get results from topical minoxidil but still want to consider oral minoxidil due to negative experiences with the topical such as scalp irritation, medication running down your neck before you can rub it in, or the hassle of applying medication two times a day.
Using both topical minoxidil and oral minoxidil at the same time will not produce better results and therefore, is not recommended.