Think of lightning as more for instant lower-value transactions. You'd use lightning if you wanted to pay for you sandwich at Subway, or tickets at the cinema. The 'standard' Bitcoin network is for everything else. If someone has send you an address that starts with 1, 3 or bc1, it's a normal Bitcoin address on the normal Bitcoin network.
You'd know if you'd get a Lightning invoice because it's much longer than a usual Bitcoin address and it starts with 'ln'.