When you are playing a single player game it is easy to narrow things down there is no random per se issues affecting it(Not everything will be exactly the same but reasonably close)
When you play an online game things are much more variable, other players can cause explosions etc that can affect your framerate for example.
When you play online there are X amount of hops between your computer and the games server which depends on your location and the game servers location. Each hop has the potential to cause a lag spike. Your ISP is only responsible for the first couple of hops. Once you are out of their network its out of their hands.
So I can not say 100% it is your internet but random drops probably are lag spikes.