In the mash, starch is converted into sugar, which is further broken down to fermentable & unfermentable sugars.
There are a lot of things going on in the mash. Like the question says, conversion is the process by which starch in the brewing grain is converted into sugar which can be used by yeast in fermentation. There are conflicting sources citing the length of conversion. Once conversion is done all the available sugars are suspended in the sweet liquor and you could proceed to mash-out.
Sugar is a broad term referring to many types glucose molecules. Conversion produces long chains of glucose, most of which are not suited to fermentation. Maltose is a simple fermentable sugar produced by beta-amylase. This enzyme attacks glucose chains from either end, splitting off a maltose. Because it only actions the ends of sugar chains longer mashes allow it to break down a chain.
Alpha-amylase breaks glucose chains at any branch. The longer alpha-amylase acts, the more ends there are for beta-amylase to get at. However, many long-chain molecules produced by alpha are unfermentable. Dextrines are one such class of unfermentable sugars.
With this knowledge the brewer can create mash conditions favoring one type of sugar or a mix. For a malty, sweet beer allow alpha-amylase to work but limit beta. To dry out your beer rest longer in the temperature & pH range where beta-amylase thrives.