In QuickBooks Online, a payment is just that, a payment for goods or services. Generally, payments are made to satisfy invoices. If no invoice is attached, the payment would be considered an "unapplied payment."
In either case, a payment only affects the balance sheet, generally reducing the A/R account balance and increasing the bank account balance.
If an invoice and a payment had a baby, it would be a sales receipt. This transaction type is generally used to reflect a transaction in real time. "I'm selling this product or service to you right now, and you're paying for it immediately."
Sales Receipts will generally affect both the income statement (P&L) as well as the balance sheet, as they typically will increase a revenue account and increase the bank account balance.