It’s less “Korra likes to use firebending and firebending-style moves.” and more “Korra uses waterbender style moves when she’s surrounded by her element, but will switch to firebender style if 1) she wants to mix it up, 2) if she’s angry or upset, or 3) she doesn’t have water on hand.” This applies to Books 1 and 2 as well as latter seasons.
Except for a few instances, Tahno almost exclusively uses a firebender style of waterbending.
A lot of the pro-bending teams use firebender style, mixed with airbender-like agility and movement.
Korra, Mako, and Bolin all use that airbender style avoidance/dodging tactic, and alternate between earthbending and firebending style moves.
While Zaheer uses classic arbender evasive maneuvers, his style of avoidance sometimes, and acrobatics mostly actually resembles Ty Lee’s style (and I’ll have a gifset on that).
For the most part, the Northern soldiers from Book 2 use classic waterbending styles of fighting, with maybe an earthbender move or two thrown into the mix, but they will switch to a firebender style of fighting depending on the situation.