Yes, but with a small distinction.
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Controller is a broad term for any device used to control video games. This includes gamepads, joysticks, steering wheels, motion controllers, and more.
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Gamepad is a specific type of controller — typically a handheld device with buttons, directional pads (D-pad), thumbsticks, and triggers, designed for use with consoles or PCs.
So:
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All gamepads are controllers, but
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Not all controllers are gamepads.
Examples:
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A PS5 DualSense or Xbox Wireless Controller is a gamepad (and thus a controller).
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An arcade joystick or a racing wheel is a controller but not a gamepad.
In casual conversation, people often use "controller" and "gamepad" interchangeably because gamepads are the most common type of controller used in console gaming.