Generally if you are going to be getting high-availability fail-over internet connections, then it would be from a different provider than your primary connection. If your primary connection goes offline for some reason it can be for many reasons. It could be physical layer, where something has affected or damaged a connection line or device from the internet provider to your connection. It could also be configuration related or even (as what happens around here often) the ISP DNS server crashes.
Many of these situations would leave a second connection from the same provider unaffected, and you'd be able to operate off of the backup connection fine. However, there are still quite a few failures that could occur at the ISP level which would affect both of your connections. This is why it's generally recommended to have your primary and backup connections be from different providers.