Sparging is rinsing the grain bed with hot water after mashing, to recover the sugar-laden liquid still clinging to and trapped between the grain particles rather than leaving it behind when the grain is discarded. Skipping it entirely is possible (see no-sparge brewing) but leaves real extract — and real efficiency — on the table.
Two genuinely different methods, not just two speeds
Fly sparging adds sparge water continuously at the same rate wort drains out, keeping the grain bed submerged the whole time and rinsing it gradually. Batch sparging drains the mash completely, adds all the sparge water at once, stirs, and drains again. Fly sparging is slower but typically extracts marginally more sugar for the same water volume; batch sparging is faster and easier to get consistent with basic equipment, at a small efficiency cost most homebrewers find an easy trade.
Water temperature matters more than most brewers assume
Sparge water run too hot (above roughly 170°F/77°C) risks extracting tannins from the grain husks, producing an astringent, puckering harshness in the finished beer that no amount of downstream process fixes. Keeping sparge water in the 168-170°F (76-77°C) range avoids that risk while still keeping the grain bed fluid enough to drain properly.