There are many people out there who are not only after healthy sweeteners but is also concerned on how their sweeteners are made. In fact, due to the human propensity for creativity, too many of the same thing is being hawked around as something else and when consumers are actually buying the same thing but having a different name.
Cane Sugar
Sugar Cane (Saccharum) is the most popular source of table sugar. It belongs to a family of grasses and is native to warm temperate to tropical regions of the world. Their fibrous stalks are stout, jointed, rich in sugar growing anywhere between 2 to 6 meters tall.
Sugarcane is stil largely harvested by hand. Hand harvesting accounts for more than half of the world's production, and is especially dominant in the developing world. When harvested by hand, the field is first set on fire. The fire spreads rapidly, burning away dry dead leaves, and killing any venomous snakes hiding in the crop, but leaving the water-rich stalks and roots unharmed. With cane knives or machetes, harvesters then cut the standing cane just above the ground. 
(Sugar cane field burning in Queensland, Australia circa 1959. Uploaded to Flickr by pizzodisevo)
Burning of sugarcane prior to harvest is done to deal with the approximately 30% residue portion of the plant. In a sample of 50 tons of sugarcane about 15 tons of residue needs to be burned and there is no currently economical way to deal with this huge volume of waste by mechanical means. Harvesting burned cane results in less waste and soil being brought to the mill
There are many sugar products derived from sugar cane: white
sugar, brown sugar (which is actually refined white sugar with molasses added), demerara, turbinado and muscovado sugars. Their
differentiation is mainly by how much or how little processing is done
on the sugar itself.
There are two categories of brown sugar: those produced directly
from the cane juice at the place of origin and those that are produced
during the refining of raw sugar. The first type includes a variety of
molasses and syrups, demerara, muscovado and turbinado sugars. The
second type is coated brown or ‘soft’ sugars, manufactured demerara,
and a variety of refinery molasses and golden syrups.
Those produced directly from the cane juice at the place of origin
can be made using relatively low-cost and low technology processes
suitable for small-scale production However, this level of production
still requires experience, skill and knowledge to be successful. The
technology involved is based on the open pan production which is
described in the Practical Action’s technical briefs on gur and the
open pan sulphitation (OPS) sugar processing.
Beet Sugar
A significant portion of the white table sugar consumed worldwide are from beets. A curious fact after refining is that no other sugar product is made but white sugar, with no taste differences from cane derived white sugar. However, no "brown" sugar is made from beets because people find the taste of beet molasses unpalatable.
The refining process is similar to that of sugar cane.
Coco Palm Sugar
These sugars are considered artisanal sugars, and a typical monthly production is just about one ton, unlike common table sugar where tons of sugars are produced daily. A palm tree may produce about 2 liters of coconut sap daily, the water is then evaporated from the sap until only the sugar solids remain. About 260 grams (9 oz) of sugar will be produced from this 2 liter sap.
A palm tree will start producing sap by its fourth or fifth year, and, barring any calamity (natural or man-made) will continue to so for the next 50-60 years. Unlike non-mechanized sugar cane harvesting which requires the burning of sugar cane fields (imagine how much CO2 is generated by burning alone) every harvest time, a coconut tree will never produce as much carbon dioxide in its own lifetime.
The annual carbon sequestration rate for a hectare of coconut trees is estimated at 4.78 tonnes of carbon.
The tappers climb the many coconut trees several times a day to ensure that only the freshest sap is harvested. (In other places, tappers may add chemical or natural anti-fermenting agents but we don't practice that.) Climbing about 20 trees a day, with trees as high as 15 meters (49 ft.) a tapper will scale 30 times the equivalent height of Mt. Everest in a month's time.
The processing is similar to that of North American maple syrups and sugar.
