I'm assuming IB = investment banking, PE = private equity, VC = venture capital, and PM = public market. To be clear, I did not work for a private equity firm itself (I do not posses the psychopathic ambition required to do so), but for a company that ended up owned by a firm; that was the terrible experience.
It was Apollo, but asking me to differentiate between them would be like the dentist asking me which drill I'd prefer; I really don't know the technical details, but they all seem very unpleasant.
PE is a broad industry, as it literally just means allocation of capital in the private market.
For example, VC is a subset of PE.
Apollo, KKR, Guggenheim, and Thoma Bravo are PE funds that have practices dedicated to acquiring non-performing assets (basically companies that are near the verge of collapse)