Private equity funds are defined as public offering and private placement, or public offering and private placement, according to the different ways of issuing securities and whether they issue securities to an unspecified public.
You can say that private equity funds are wealth management products, but you can't say that wealth management products are private equity funds; This is like saying that pigs are animals, but not animals. I think what you want to express should be public offering or private offering. At present, most of the wealth management products mentioned by everyone are for the public and belong to the type of public offering, but they are not necessarily funds.