Sugar is a general term but usually refers to sucrose (table sugar), the disaccharide of glucose and fructose bound together. Invert sugar is made when a dilute acid and heat is used to break the glycosidic bond with the liberated monosaccharides of glucose and fructose. Regardless, both will remain soluble in a solution of 80% methanol and 20% water.
Starch is also a general term and can refer to many forms of starch or starch products (especially when listed on the ingredient list). If it is uncooked "native" starch then it will be in a granule form totally insoluble, and will precipitate in 100% water without needing freezing, only sufficient time. Granular starch is visible under a microscope and this can usually help to determine the botanical type of starch it is (ie corn, potato, wheat, tapioca, rice, etc) based on its size and shape. If the starch has been heated above that botanical type of starch's gelatinization temperature, then it will no longer be in the granule form as the granules rupture and the polymer molecules of amylose and amylopectin (both very long chains of glucose) become solubilized in the aqueous solution and this is accompanied with a dramatic increase in solution viscosity. However, in a solution of 80% methanol and 20% water, these polymers will precipitate losing all viscosity, so this is an easy way to separate the sugars from any water-soluble polymers such as amylose and amylopectin. When these polymer molecules are precipitated and dried to a powder again, this is called pregelatinized starch (as used in instant puddings).
However, another form of starch still is called maltodextrin, which is either acid or enzyme (amylase) digested starch. Here the amylose and amylopectin polymers are degraded to much smaller molecular weight chains of glucose (on average about 10 glucose units) so maltodextrin is very soluble in water. With a 80% methanol and 20% water solution, much of the maltodextrin will remain soluble with any sugars, but some of the largest digested chains of glucose will precipitate. Separating the smaller, most soluble fragments of maltodextrin will be very difficult without using something like column chromatography or some other advanced method. If your starch solution in water is non-viscous when above 2% concentration, then it is likely maltodextrin as the form of starch in solution (if as you say it is fully soluble -- no granules).
A simple test for seeing if your separation was successful is using an iodine solution (tincture of iodine from medicine cabinet) and dripping into the sugar and starch solution. If there is any granule starch, pregelatinized starch or maltodextrin in your solution it will turn a purple-blue colour (if amylose and amylopectin are in solution) or a pinkish-red colour (if only amylopectin without amylose is in solution with this called waxy starch). If there is only a sugar solution, it will not turn bluish-purple or reddish-pink, only a very faded yellow-brown colour as the original colour of the iodine solution is.
Here is a short video showing the heat gelatinization of potato starch granules into solubilized amylose and amylopectin, if you are interested:
https://www.youtube.com/watch?v=Kl95yJ3tnA4