"Demand-pull inflation" refers to the effects of falling unemployment rates (rising real gross domestic product) in the Phillips curve model, while the other two factors lead to shifts in the Phillips curve.
The built-in inflation originates from either persistent demand-pull or large cost-push (supply-shock) inflation in the past.
It then becomes a "normal" aspect of the economy, via inflationary expectations and the price/wage spiral.
It means that the standard methods of fighting inflation using monetary policy or fiscal policy to induce a recession are extremely expensive, i.e. they can cause large rises in unemployment and large falls in real gross domestic product.
This suggests that alternative methods such as wage and price controls (incomes policies) may also be needed in the fight against inflation.