Wi-Fi extenders, also known as Wi-Fi boosters or repeaters, are largely the same thing under a different name. If you have areas of your home where your current wireless internet cannot reach, they're the perfect piece of kit to boost your existing signal.
They're typically easy to use and set up, with most simply plugging into an available AC outlet in your wall, though some can resemble a stand-alone router.
Naming conventions appear to be a branding decision, but there are a few different ways that Wi-Fi extenders work. The most common is that your booster or extender houses two wireless routers, much like the wireless router you already have at home, or in your place of work. One of these wireless routers picks up the existing Wi-Fi network and then passes that to the secondary router which transmits the boosted signal.
It's worth noting that many Wi-Fi extenders broadcast on a new Wi-Fi network with its own name, so you'll need to connect to a different Wi-Fi signal depending on where you are in your home. As most devices will automatically connect to a trusted signal, this isn't likely to cause too much of an issue.