OK, let's try to clarify this simply.
1. If you want to pay with a debit or credit card, or digital wallet (PayPal or Click to Pay) you are limited to two payments per period. The period changes depending on what you are paying. So if you are paying taxes for the year (last year, prior year or next year; or an installment agreement, estimated tax, or extension), you can only make two payments for the year. If you are paying for the quarter (for example, if you are paying estimated taxes for that quarter), you can make up to 8 payments for the year (4 quarters x 2 payments maximum for the quarter). Any other kind of tax filings and forms will probably not apply to you, but if they do, you are probably in such a complicated situation that you will need an accountant anyway, so don't worry about it. Please note that these payments are only handled by three companies with nearly identical rates (extra charges added to the amount owed to cover handling fees).
2. If you don't need or want to use method 1, your next best choice is probably direct payment/debit of the amount from your bank, either a checking or savings account. This is comparable to writing an electronic check (no paper needed). These payments are all limited to two per 24-hour period, regardless of the type of tax you are paying. This comes to virtually 730 payments a year (365 x 2), or 732 in a leap year. Not unlimited, but close enough. Hours are limited, presumably for maintenance and the like, but they are accessible every day, and most people are asleep when they are inaccessible. Oh, and this is where the $10 million limit comes in (doesn't apply to me, but again, if it applies to you, you should be on your yacht drinking martinis while your accounting department sweats this stuff). There is no charge for this, unless it comes from your bank.
3. Finally, there is the EFTPS, or Electronic Federal Tax Payment System. I only mention it as an alternative, even though no one asked about it. Also free, but you have to pre-enroll in the service to use it, since it asks for additional identifications (this is because it isn't used just to make a payment, but allows you to change or cancel scheduled payments, track payments, view up to 15 months of payment history, and get help with payments or questions from Customer Service Agents.
All of this information can be retrieved from the horse's mouth, at the IRS webpage https://www.irs.gov/payments/pay-your-taxes-by-debit-or-credit-card, with links to the various payment methods. Feel free to read it as often as you want.
