Falcon 9 (not heavy) has a first stage and a second stage. The first stage consists of one kerosene tank, one oxygen tank and nine engines. This is also called

Falcon 9 (not heavy) has a first stage and a second stage. The first stage consists of one kerosene tank, one oxygen tank and nine engines. This is also called a core. Falcon 9 heavy (no crossfeed) has a first stage and a second stage. But the first stage consists of 3 cores that run in parallel. All three cores start and stop at the same time. So 27 engines start at the pad. Falcon 9 heavy with crossfeed has sort of two or three stages, depending how you count. Outwards it looks very similar to the no-crossfeed Falcon 9 heavy. The topmost stage is similar to the two already mentioned configurations. The three cores look pretty similar. All three cores start at the pad (27 engines running), but the propellant for the center core's engines is taken from the outer cores' tanks. This means the outer cores run out of propellants quite quickly. They can then be discarded in flight, and the center core starts using propellants from its own tanks. Now it can fly without the dead mass of the outer cores and as a result the rocket can carry a bigger payload. Why start the core engine at the pad, and not make it a real second stage that starts up only higher? Because then you get more thrust, the engines are not dead weight during early flight. Some rockets like Titan IV had a somewhat similar parallel configuration but they did not start their center engine except at high altitude.