First there is the Coffee Maker which is traditionally the drip-filter type of machine that allows heated water to drain naturally through a bed of ground roasted coffee beans.
Second there is the Espresso Machine which forces steam through a (usually) pressed bed of ground roasted coffee beans to draw more flavor out of the beans than with the drip-filter type.
Third there is the Combination machine which performs both functions satisfying those in the household who like one of the methods above of coffee-making and those who like the other.
There are variations within each category, for example the Plunger type coffee makers such as the Bodum French Press range in which the hot water is forced through the coffee grounds (ground to a special size) by hand pressure on the plunger. Then there are the Moka type Espresso machines which may be considered as part of the Percolator type variations within the Espresso machines where the boiling water is forced through the coffee grounds (again ground to another special size) by steam pressure produced by heating the Espresso machine on an element or even over a fire.