The "Double Shock" term typically refers to the rumble or vibration feature in PS4 and PS5 controllers. The DualShock 4 (PS4) and DualSense (PS5) controllers both offer this feature, along with motion sensors and a built-in speaker. The DualSense also introduces haptic feedback and adaptive triggers for a more immersive experience. 
PS4 DualShock 4 Wireless Controller:
Connectivity: Wireless (Bluetooth).
Features: Motion sensors (accelerometer and gyroscope), built-in speaker, stereo headset jack, vibration feedback (rumble), light bar.
Power: Rechargeable battery (often Lithium Polymer). 
PS5 DualSense Wireless Controller:
Connectivity: Wireless (Bluetooth).
Features: Haptic feedback, adaptive triggers, built-in microphone, motion sensors, built-in speaker, touchpad, light bar.
Power: Rechargeable battery.
Additional Features: Can be used on PC and mobile devices via Bluetooth or USB-C. 
Key Differences Between DualShock 4 and DualSense:
Haptic Feedback and Adaptive Triggers: These are the most significant upgrades in the DualSense, providing a more realistic and interactive gaming experience. 
Design: The DualSense has a slightly different shape and button layout compared to the DualShock 4. 
Connectivity: The DualSense can connect to PCs and mobile devices more easily.