"Plush" is a descriptive term, there's no such thing as plush with regards to a coat type. There's a true longcoat (no undercoat), which is fairly rare, there is a regular stock coat, and a long stock coat (with undercoat). That's all. Stock coats and long stock coats can vary in length and thickness.
Sometimes when people refer to a plush coat they're talking about a thick show coat, which is still just a stock coat. Other times people refer to a long stock coat as a plush coat, which can get confusing.
I have two coaties - one with a longer, shinier coat, and the other with a shorter, thicker, plusher feeling coat. But they're both just long stock coats.