Then perhaps your first sentence should have read, "Rocket packs are officially dead".
I think that the terms have historically been used interchangeably, but the distinction should be made. It's awfully nice not to need to carry oxidiser for your propellant.
A rocket is something with only an exhaust. A jet also has an intake. And it goes a little further than just not lifting the 02. Any unburnt gas (air) becomes a 'working fluid' that can be pushed. A rocket moves by throwing gas away at speed. Jets also grab gas from the air and accelerate it along with exhaust products. That's why a jet or turbofan can have a high specific impulse with such a low exhaust velocity, higher (>8k) than even an ion thruster in vacuum.
I think that the terms have historically been used interchangeably, but the distinction should be made. It's awfully nice not to need to carry oxidiser for your propellant.