If I buy a Fiber connection from an ISP and a cable connection form that same ISP would the connections be on a different networks. I will be using the Fiber connection to be my primary internet connection, and the Cable connection is my secondary connection. My concern is if there was an outage could it bring both connections down since they are from the same ISP.
Usually when you sign up for an internet connection from an ISP they will connect you with the cable system that is available in that city or town that you live in. I've not heard of an ISP company that would have both fiber and cable and if they do then wouldn't it be very expensive to get both connections and just have one as a back up?
Anyway if you did do as you say then the company will have just the one network connection on thier end and when the internet goes down there are several reasons for that and one could be the cables on the pole being damaged and it would be if both cables were damaged that you would lose both services , but if one cable was damaged and the other not then you would still have one active. If the ISP lost thier connection to the infrastucture then you lose both types fiber and cable.
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.