Both sugar and salt are needed for plant growth.
But first a distinction needs to be made between what is meant by "sugar" and "salt". In the home context salt refers to Sodium Chloride (NaCl) or normal table salt; refined and granulated sugar is normally sucrose (a Disaccharide) which is a carbohydrate.
In Biological context:
- In botany and chemistry the term salt means an ionic compound resulting from neutralization, so you get Calcium salts, Sodium salts, Magnesium salts etc. Most of these elements are used in the normal metabolic processes of plant cells - so yes, plants do use "salts".
- Sugar (as with salt) can mean a variety of things as it also a generic term and covers simple sugars (Monosaccharides) and complex sugars (Disaccharides). Sugars are essentially Carbon-Hydrogen-Oxygen compounds and an array of them are produced during the photosynthetic process.
The elements in normal table salt (NaCl - Sodium Chloride) are both used by the plant in its metabolic process, but in very small amounts - normally measured in parts per million (ppm) of concentration. Adding table salt to the soil upsets the osmotic potential of the soil water (as well as the pH)- this prevents water from being drawn into the plant so most plants will wilt and die - even at relatively low levels.
Certain plants are adapted to living in saline soils and have specific mechanisms which enable them to extract water and process high levels of salt. These plants are normally termed halophytes.
Sugar can in fact have short term benefits to plant growth, however the long term effects can prove fatal. Accumulation of sugar in the soil provides the ideal breeding environment for bacteria and fungi, some of which can invade and attack the plant.
It's best not to experiment with either on plants you want to keep. Salt added to the ground will render it useless to almost all plants.
If you want to experiment do it with plants in a pot so as not to contaminate your ground.