Generic explanation incoming.
Sugar means lots of things. Monosaccharides (single sugar molecules: chiefly glucose, fructose, galactose), then there are disaccharides which are combinations of two monosaccharides (e.g. lactose, sucrose, maltose). Polysaccharides are lots of linked monosaccharides, such as starch (in plants) and glycogen (in animals) for glucose storage. And plenty more sugars, but let's skip all that. Disaccharides are broken down into monosaccharides in the gut, which are then absorbed in the gastrointestinal system.
Table sugar (typical refined sugar) is sucrose, which is glucose + fructose. Fruit has mostly fructose. Milk mostly lactose, which is glucose + galactose.
Glucose is the basic form of sugar which biological organisms tend to use for energy metabolism. As a result, it is taken up by all cell types in the body for their energy, and this also why it's important in blood supply: thus blood glucose, glycaemic index, control via insulin (and glucagon) and relevance for diabetes. Fructose and galactose, however, are not metabolised across the body, but in the liver, where they are mostly converted into glucose, glycogen, or fats which can then be transported and used by other cells in the body. Glucose therefore has a much higher glycaemic index than fructose and galactose, obviously so, because glycaemic index represents blood glucose and absorbed glucose goes straight into the blood. Fructose and galactose only result in limited glucose production and release.
However, there are some major issues not really being covered here. High levels of monosaccharides are not good for the body, because sugars do other things too. For instance, they bind to other molecules in the body such as proteins (this is the source of the HbA1c test for diabetes, which measures glucose binding to haemoglobin), which is often not a good thing as they can impair their function. We're relatively well adapted to glucose, but much less so to fructose and galactose: they tend to be even worse than glucose in this regard of binding to molecules we'd be better off them not binding to. There's another problem that fructose and galactose: being metabolised in the liver into fats can contribute heavily to fat accumulation, particularly in the liver itself with risk of liver impairment, plus significant production of waste metabolites that may also be problematic.
So yes, the metabolism of various sugars is different. However, the long and short of it is that whilst you might argue that fructose and galactose are better for humans with respect to glycaemic index and diabetes risk, studies suggest that they're associated with outcomes equivalent to, potentially even worse, than glucose in terms of overall population health (although there may be varied advantages and disadvantages at the level of individuals).
So, my basic suggestion would be to be mindful of sugar consumption from any source whatsoever, and I would be extremely cautious of advice suggesting fructose is somehow "safer" than sucrose.