My understanding is that a booster is a device which receives your wifi signal and then re-transmits it. If your pc is in a bedroom and your router is in the hall, a booster sited between them would improve the signal in the bedroom. An extender plugs in near your modem, with another one near your computer. You connect your modem and computer using ethernet cables.
I have my modem in the hall and my main computer in a bedroom, which I prefer to connect with cables rather than wirelessly. I connect the modem to an extender in the hall and my router (in the bedroom) to the other extender. I can then connect my PC to the router via an ethernet cable and use my laptops wirelessly anywhere.