heavy cavalry engaging heavy cavalry

[Domen]

The term "line cavalry" implies the standard cavalry of the time

Sorry but no, not according to Digby Smith's typology at least.

Digby Smith counts dragoons, mounted grenadiers and carabiniers as line cavalry.

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hussars

Hussars was a name applied to a few different cavalry formations. Early hussars were basically light lancers, Polish husaria since the 2nd half of the 16th century were heavy cavalry, while 18th and 19th century huzars were light cavalry. Three very different formations belonging to three different types of cavalry.

Early hussars originated in Serbia, later this cavalry was adopted in Hungary and in Poland. When Polish hussars transformed into heavy cavalry, they abandoned shields but started wearing armour.