In the United States, the everyday term is "ground coffee." Ground coffee is an insoluble brown powder. It is ready for use in a coffeemaker. There are many kinds of coffeemaker but they all involve adding very hot water to the ground coffee, letting it steep, and then filtering it to separate the brewed coffee from the grounds.
Soluble coffee, which is much less popular than it used to be, is called "instant coffee."
"Bean coffee" means whole coffee beans that have been roasted, but need to be ground in a coffee grinder before brewing.
The most popular way to brew coffee at home is an "automatic drip coffeemaker." It is an electric appliance with a water reservoir. There is a "brewing basket" open at the top, with a hole in the bottom. Under the hole is a "carafe" to receive the brewed coffee. You line the basket with a paper filter and put ground coffee into it. As the water boils, the steam propels the water up through a tube. It drips gradually over ground coffee, and then streams slowly out of the hole in the bottom and into the carafe.
Coffee brewed from grounds is sometimes called "perked coffee," to distinguish it from "instant coffee." One of the devices for making coffee is a "percolator," hence "perked." It would be natural to say "instant coffee is better than nothing, but it nowhere near as good as perked coffee."
More and more people are using "K-cups," the trademarked name for a system made by Keurig, which uses small sealed plastic cups containing a pre-measured amount of ground coffee. The system is convenient because it allows you to brew a single cup of fairly good coffee quickly, and thus allows you to have an assortment of different kinds so that one person can have a cup of decaf, another a cup of regular coffee, and another a cup of dark roast coffee. It is very expensive to use, and creates a large amount of waste in the form of used plastic K-cups.