Throughout The Witcher series, many different military units exist, sometimes changing names depending on the country.
In the real world a banner was usually associated with a unit between 200-400 troops; it is possible that infantry banners exist and possibly fall on the upper end of the scale due to the comparative inexpensiveness of foot soldiers.
A division is a formation within an organized army or large military unit.
A free company refers to an army of mercenaries (or condottieri) officially acting independently of any government, for whoever will pay, thus the word "free" in their name meaning free of any particular allegiance. This type of mercenary group is most popular in Redania.
In The Tower of the Swallow, king Esterad Thyssen of Kovir and Poviss released some political prisoners formerly known as the "Sly cats" on the condition that they support the efforts to push back the Nilfgaardian invasion at the battles of Mayena and Brenna.