Sugar as a generic term is any sweet carbohydrate.
"Table Sugar" or commonly used by most as "Sugar" and specifically refers to Sucrose. A disaccaride made up of Fructose and Glucose.
HFCS is a solution of fructose and glucose chemically made from starch. Starch is long chains of glucose. Gets cut up by enzymes and enzymes convert glucose to fructose. The ratio of Fructose to Glucose in HFCS can be specified, but usually used as around a 50:50 ratio to mimic sucrose.
So HFCS has sugar in it, but technically no sucrose in it, but it's made up of the same individual monosaccarides Fructose and Glucose.
Put sucrose in your stomach, and it breaks down into glucose and fructose due to your stomach acid.