MobilePay Online is essentially a way for the user to accept eCommerce/online payments in the MobilePay app. When the user accepts the payment, their card data is transferred to the PSP who can then do the authorization towards the acquirer chosen by the web shop.
You can find an example of a MobilePay Online flow here.
MobilePay is a digital wallet for iOS and Android that can be used for person to person transfers, in-store purchases, subscriptions, invoices, eCommerce transactions etc. The documentation on this page covers the technical setup of the eCommerce functionality and is directed at Payment Service Providers that wish to offer MobilePay as a payment method to their customers (i.e. web shops).