A turbofan and a turbojet are very similar, yet two different systems.
You sure about that? Are you sure a turbofan isn't a turbojet with a fan on the front?
Traditional turbocharging boosts air pressure as high as 40 inches of manifold pressure. Turbo-normalizing only allows the air pressure to build to about 30 inches.
Turbo-normalizing means the engine holds sea level pressure as it climbs rather than resorting to high turbo boosted pressures (up to 40 inches) with low compression ratio piston configurations like traditional turbochargers.
So, yes they are nearly identical, but differences do exist.
You need to seek a little more education on the subject.
A turbocharged engine which boosts to sea level pressure is said to be turbonormalized...but is still turbocharged.
A turbocharged engine which boosts to a 32" Hg pressure is a turbocharged engine. A turbocharged engine which boosts to a 40" Hg pressure is a turbocharged engine. A turbocharged engine which boosts to a 29" Hg pressure is a turbocharged engine.
If one uses a turbocharger to boost manifold pressure, but relieves that pressure at a given value, one is still turbocharging the engine...which is exactly what is happening in a turbonormalized engine.