No. The model you purchase will determine which trigger type your controller will have.
Reflex and Reflex Pro come equipped with adaptive triggers, which are native to the DualSense. These can be configured from the PlayStation console settings.
Adaptive triggers allow you to experience varying levels of force and tension as you interact with your in-game gear and environments (pulling back a bowstring, pressing the brake pedal while in a car, pulling the trigger of a weapon, etc.).
Reflex FPS will come with Instant Triggers, which act like a mouse click for faster reaction.
The Reflex FPS replaces the full-pull adaptive trigger with our dedicated Instant Triggers that provide a short mouse-click action. This hyper fast, limited motion is perfect for your favorite shooter games and getting those quick reaction shots off faster.
Please note: We recommend only using Instant Triggers in shooting games, as some games require the full trigger motion to function properly.