It's the same type rating in England but not here. The HS-125 covers the "A" and "B" models only. The 1,000 is a "C" model. It's not the increased engine thrust or extra fuel capacity, 1,300 lbs, that did it, but the fact that the engines are not linked via cables at all but are computer controlled like the Lear 45. (TLA)-Thrust lever angle. Also, the inverter panel has been removed.
If you do already have an HS-125 type rating and are current, within the last 12 months, Simuflight can get you trained in five days; for what it's worth.