What is the difference between Instant coffee and filtered coffee?

Instant coffee is pre brewed coffee ready to rehydrate with boiling water. It dissolves and is ready to drink with no residue.
Filter coffee is ground roasted beans through which you pour boiling water and the liquid is passed through a filter leaving only the fresh brew. The grounds stay trapped in the filter.

Two of the 50 known species of coffee beans dominate the beverage coffee industry. Coffee arabica varieties, grown primarily in Latin America, India, and Indonesia, are relatively mild in flavor and, consequently, bring a higher price. They are also relatively expensive to harvest, since individual coffee cherries must be hand picked at their peak of ripeness. Coffee robusta varieties, grown mainly in Africa, India, and Indonesia, have a harsher flavor, but they are cheaper to grow since they can be harvested over a range of ripeness and are more resistant to diseases and insects. Because of their more attractive price, the robustas are widely used in the manufacture of instant coffees.

Roasting at temperatures above 300°F (180°C) drives the moisture out of coffee beans. Beans destined for use in instant products are roasted in the same way as beans destined for home brewing, although the moisture content may be left slightly higher (about 7-10%). The beans are then ground coarsely to minimize fine particles that could impede the flow of water through the industrial brewing system.

The Manufacturing Process
Extraction•1 The manufacture of instant coffee begins with brewing coffee in highly efficient extraction equipment. Softened water is passed through a series of five to eight columns of ground coffee beans. The water first passes through several "hot" cells (284-356°F, or 140-180°C), at least some of which operate at higher-than-atmospheric pressure, for extraction of difficult components like carbohydrates. It then passes through two or more "cold" cells (about 212°F, or 100°C) for extraction of the more flavorful elements. The extract is passed through a heat exchanger to cool it to about 40°F (5°C). By the end of this cycle, the coffee extract contains 20-30% solids.
Filtration and concentration•2 After a filtering step, the brewed coffee is treated in one of several ways to increase its concentration. The goal is to create an extract that is about 40% solids. In some cases, the liquid is processed in a centrifuge to separate out the lighter water from the heavier coffee extract. Another technique is to remove water by evaporation before cooling the hot, brewed extract. A third alternative is to cool the extract enough to freeze water, and then mechanically separate the ice crystals from the coffee concentrate.
Recovery of aromatic volatiles
•3 Part of the enjoyment of making and drinking coffee is smelling the aroma. During the several steps of the manufacturing process, volatile aromatic elements are lost; they must be returned in a later step to produce an attractive instant coffee product. Aromatics can be recovered during several stages of the manufacturing process. For instance, gases released during the roasting and/or grinding processes can be collected. Ground, roasted coffee can be heated to release additional aromatic gases. Passing steam or appropriate solvents through a bed of ground, roasted coffee can strip and capture aromatic components. Aromatic oils can be expressed from spent coffee grounds by exerting pressure of at least 2,000 lb per sq in (14,000 kPa). Gases can also be distilled from coffee extract after the brewing process is complete.
•4 To preserve as much of the aroma and flavor as possible, oxygen is removed from the coffee extract. This is accomplished by foaming other gases, such as carbon dioxide or nitrogen, through the liquid before it enters the dehydration phase of the manufacturing process.
Dehydration
Two basic methods are available for converting the liquid coffee extract to a dry form. Spray drying is done at a higher temperature, which affects the taste of the final product, but it is less costly than freeze drying.

Spray drying•5 Cooled, clarified liquid concentrate is sprayed through a nozzle at the top of a drying tower. The tower is at least 75 ft (23 m) tall. Air that has been heated to about 480°F (250°C) is blown downward through the mist to evaporate the water. The air is diverted out of the tower near the bottom, and it is filtered to remove fine particles, which can be recirculated back through the tower or reintroduced during the agglomeration step. The dry coffee powder collects in the bottom of the tower before being discharged for further processing. The resulting powder contains 2-4% moisture and consists of free-flowing, non-dusty particles.
•6 Spray drying may be followed by a step to form the powder into coarser particles that will dissolve more completely in the consumer's cup. The agglomeration process basically involves rewetting the surfaces of the coffee powder particles and bringing the particles into contact, so that they will adhere to each other and form larger, more granular particles. This is accomplished by exposing the powder to steam or a fine mist, while tumbling it in the air.
Freeze drying•7 Freeze drying may be used instead of spray drying. The process involves four steps, beginning with "primary freezing." Coffee extract is chilled to a slushy consistency at about 20°F (-6°C).
•8 The prechilled slush is placed on a steel belt, trays, or drums and further cooled in a series of steps, until it reaches a temperature of -40-(-50)°F (-40-[-45]°C). Quick cooling processes (taking 30-120 seconds) result in smaller, lighter colored products, while slower processes (taking 10-180 minutes) generate larger, darker granules.
•9 The slabs of ice are broken into pieces and ground into particles of the proper size for the drying step. The particles are sieved to ensure proper sizing, and those that are too small are melted and returned to the primary freezing stage.
•10 The frozen particles are sent into a drying chamber where, under proper conditions of heat and vacuum, the ice vaporizes and is removed.
Aromatization•11 Volatile aromas that have been recovered from earlier steps in the manufacturing process are sprayed on the dry coffee particles. This may be done during the packaging operation.
Packaging
•12 Instant coffee particles are hygroscopic—that is, they absorb moisture from the air. Consequently, they must be packaged under low humidity conditions in a moisture-proof container to keep the product dry until purchased and opened by the consumer. Also, to prevent loss of aroma and flavor, the product is packaged in a low-oxygen atmosphere (usually carbon dioxide or nitrogen).