Why the Confusion? They're Related, After All!
2. Exploring the Interdependence of Continuity and Current
Okay, I get it. You're probably thinking, "If you need continuity for current, then aren't they basically the same thing?" Not quite! Think of a light switch. When the switch is off, there's no continuity in the circuit, and therefore no current. Flip the switch on, and suddenly, BAM! Continuity is established, current flows, and the light bulb shines brightly. The switch controls the continuity, which, in turn, allows or prevents current flow.
Consider another example: a corroded wire. Initially, there might be continuity, but the corrosion increases resistance. This resistance impedes the flow of current, like a clogged pipe restricting water flow. Eventually, the corrosion might completely break the connection, leading to a loss of continuity and, naturally, no current.
Think of continuity as the potential for electricity to do its thing, and current as electricity actually doing its thing. One's the promise, the other's the delivery. Just because you could drive somewhere (continuity), doesn't mean you are driving there (current).
Essentially, continuity is a necessary condition for current, but it's not sufficient on its own. You also need a voltage source (the "push" that drives the current) and a load (something that uses the current). Without all three, you've got continuity doing nothing.